Transmission of a message via quantum communication with eavesdropping detection

Abstract

Transmission of a message by quantum communication with eavesdropping detection Quantum communication system (1) comprising: an entangled photon emitter (2), comprising a source configured to generate at least one pair of entangled photons comprising a first photon (P1) emitted on a first propagation path (D1), and simultaneously a second photon (P2) emitted on a second propagation path (D2) different from the first propagation path; a first receiver (3) disposed on the first propagation path (D1), comprising a complex absorber (31) configured to absorb the photon in a polarization state selected from the states of at least two different pairs of complementary polarization states;a second receiver (4) arranged on the second propagation path (D2), comprising an optical amplifier (40) allowing the second photon (P2) to be multiplied while preserving its polarization and a measuring instrument (45) allowing the average polarization of the multiplied photons (P20) to be measured. Figure for the abbreviation: Fig.1A;

Description

Title of the invention: Transmission of a message by quantum communication with listening detection Technical field

[0001] The present invention relates to methods of transmitting a message by quantum communication with eavesdropping detection, and more particularly to methods of transmitting a message by quantum communication using entangled photons with eavesdropping detection by cryptography. Prior Art Cryptography

[0002] Computers and electronic devices are often connected to a network, physically, wirelessly, by RFID, or by any other secure or insecure means, and sometimes need to be able to know the identity of the device that sent them certain data, for example to ensure that this data has not been transmitted by another device, which has intercepted and modified it before sending it back to the rightful recipient, or simply to identify without a shadow of a doubt the identity of the sender of the data, which is for example an automobile on a road network or an RFID tag worn by a competitor during a sporting event, or a list of bits randomly generated by a Quantum Key Generating Device (QKD), or for any other reason for which the identity of the sender of the data is important to the recipient.

[0003] Quantum Key generating devices often use electronic signatures exchanged between two remote parties receiving a randomly generated key to ensure that the received key is the same for each party. However, advances in quantum computing and / or cryptography may make it possible to recover the keys used for electronically signing received keys, allowing the supposedly secret key to be shared between a legitimate device and a non-legitimate device without the legitimate device noticing.

[0004] Transmitted data can be sent fully encrypted using a key assigned to the sender. However, encrypting all data makes it difficult to use one-time keys (block-once keys). More specifically, full data encryption is a method that uses keys as long as the data they encrypt, and these keys must be renewed after use.

[0005] It is therefore necessary for computers or other electronic devices communicating, for example by exchanging text, identifiers, numbers, computer programs, images or video or audio codes, to verify the identity of the sending device by using encryption of an amount of data smaller than the amount of data sent. For this reason, an electronic signature is used, consisting of encrypting a hash of the data. The term "hash" is used to designate the result of a hash function which, based on an initial data input, calculates a fingerprint used to quickly, although incompletely, identify the initial data. It is common to send, with the data, an encrypted hash which will then be decrypted by the recipient and then compared to the hash of the received data. MD5, SHA1 and SHA256 are algorithms commonly used for these hashing operations.However, data hashes are usually much smaller than the original data, and it may be possible to create other data, similar but slightly different from the original data, whose hash is equal to the hash of the original data. This data could therefore be substituted for the original data, without being rejected by the hash verification procedure. It is possible to substitute data of any type, but the user detectability of the substitution decreases as the complexity of the data increases (a long text, an audio file, a photo or a video). To perform the substitution, it is not even necessary to decrypt the encrypted hash. It is sufficient to calculate the hash of the original data. In addition, hash functions such as MD5 and SHA1 are hash functions that are currently relatively easy to circumvent.

[0006] Quantum computers currently under development should soon be able to bypass the security provided by hash functions, since they are able to optimize the starting files in such a way that they have a predefined hash.

[0007] Methods for improving the security of systems using hashing techniques are known from the prior art.

[0008] Patent application CN101547184 uses a plurality of auxiliary authentication values ​​that are exchanged between a server and users.

[0009] In the method proposed in patent application US2011 / 0246433, a hash of the data to be sent is generated and concatenated with the fragment of data to be sent and a randomly numbered label.

[0010] Patent application EP 1 421 548 describes a method for transmitting information, in which a message to be sent is concatenated with a random number and then hashed. The result of the hash is sent unencrypted to the other party. The message is sometimes transmitted as is or encrypted. The random number is always transmitted signed, and optionally encrypted, to the other party. Not encrypting the hash when the message itself is not encrypted makes the transmission vulnerable to very powerful or quantum computers capable of calculating numbers random numbers consistent with the unencrypted message and the hash result. Moreover, encrypting the entire message has the disadvantage, if this encryption uses block-once keys, which are supposed to be unbreakable, of requiring that both corresponding parties have access to these shared keys. Quantum communication

[0011] The transmission of information is currently carried out essentially using electromagnetic waves, whether these have short wavelengths, such as light, or long wavelengths such as VHF waves.

[0012] The transmitted waves can be guided by metal cables, by optical fibers, or transmitted through space.

[0013] These methods use wave propagation to transmit energy and therefore physical particles which, collected by a receiver, make it possible to deduce information, which is coded, for example by its wavelength or by modulation of the duration of the wave trains.

[0014] Recently, so-called "quantum" communication methods have been developed.

[0015] For example, the physical state of a photon, such as its polarization, can be used to transmit information, for example via an optical fiber. The value of a bit is arbitrarily assigned to a direction, or to a polarization mode of the photon. Sequences of polarized photons can then be sent to transmit binary sequences making up a message.

[0016] In the context of quantum cryptography, it is known in particular to use a pair of entangled photons to transmit information securely. Entangled photons are photons whose quantum states, for example their polarization, depend on each other, regardless of the distance separating them.

[0017] This phenomenon of quantum entanglement has been observed and demonstrated experimentally on several occasions, such as in the article by Shasi Prabkhar et al. “Two-photon quantum interference and entanglement at 2.1 pm” (Sci Adv, 2020).

[0018] Patent KR101003886B1 describes a system for transmitting encrypted information in which entangled photons are emitted simultaneously and each sent to two targets positioned at different locations and wishing to communicate with each other. The photons received by the two targets form random entangled sequences of conjugated bits, these sequences being used as cryptographic encryption keys. This system allows the almost instantaneous reception in two different locations of the same sequence of random numbers but does not allow the transmission of information.

[0019] Wang's article "Superluminal telecommunication: an observable contradiction between quantum entanglement and relativistic causality" discloses a quantum communication system enabling superluminal information transmission using a pair of entangled photons sent to two receivers wishing to communicate. communicate with each other. The photons are entangled, and a linear polarization is measured for the photon arriving at the first receiver from different directions at 45° to each other. At the second receiver, the second photon is demultiplied and the average polarization of the demultiplied flux is measured to determine in which direction the first photon was measured.

[0020] The polarization of a photon is however not necessarily binary like that of a spin or even quaternary. It can in particular be represented on the Jones sphere which characterizes the orientation and the ellipse of the polarization: a polarization can in fact be linear, the electric field always being parallel to an axis perpendicular to the direction of propagation of the photon, or circular, the electric field rotating around this axis, or between the two: the electric field traveling an ellipse around the axis of propagation. In the case where the polarization is not circular, the orientation measures the direction of this axis, and the eccentricity measures the flattening of the ellipse.

[0021] The aforementioned devices do not allow all polarization configurations to be used and are in fact limited in the number and type of information that can be transmitted. Statement of the invention

[0022] There is a need to further improve quantum communication systems and methods to take advantage of entangled photons and to prevent and detect eavesdropping during entangled photon communication. Summary of the invention

[0023] The invention aims to meet this need and achieves it, according to a first of its aspects, by means of a method for transmitting a message M by quantum communication from a first receiver to a second receiver with listening detection, the transmission and detection method comprising the steps consisting of:

[0024] (A) generating a series of Np pairs of entangled photons from an emitter, the the first photon of each pair being emitted towards the first receiver on a first propagation path and the second photon of the pair being emitted simultaneously towards the second receiver on a second propagation path, the first and second photons being entangled, the second receiver being located on the propagation path of the second photon further from the transmitter than the first receiver, such that the second photon arrives at the second receiver after an additional travel time t^,

[0025] (B) converting the message M into a series of Ni information I to be transmitted in a first predetermined numbering base,

[0026] (C) at the first receiver, for each information I: a. for each entangled photon, modifying the polarization state of the first photon when it reaches the first receiver into a polarization state dependent on the information I to be transmitted, the polarization state being selected from at least two different pairs of complementary absorption polarizations, and b. using an absorption instrument, absorb the first photon in one of the two complementary polarizations of the selected pair,

[0027] (D) to the second receiver: a. duplicate each received photon into a stream of multiplied photons using an amplification device, the light which is created having preserved the polarization state of the photon, b. measure, for each duplicated photon, the average polarization state of the luminous flux, and c. determine according to this measurement the polarization state of the first entangled photon received by the first receiver, in order to deduce the information I which could have been transmitted by the first receiver, d. adding an element comprising the reception time of the second entangled photon and the determined polarization state of the first entangled photon which may have transmitted the information I, to a deduction list, the deduction list being a list comprising the reception times of the second entangled photons and the determined polarization states of the first entangled photons which may have transmitted the information I,

[0028] (E) implementing a listening detection method,

[0029] (F) deduce from the deduction list the transmitted message M,

[0030] the listening detection method implemented in step (E) comprising a shared quantum key generation method comprising the following steps:

[0031] (G) the first receiver establishes a first list comprising the dates of reception to the first receiver and a second list comprising these reception dates and the relative polarization states of the photons absorbed by the first receiver, and the second receiver establishes a third list comprising the reception dates at the second receiver and a fourth list comprising these reception dates and the relative polarization states of the photons received by the second receiver,

[0032] (H) the first list and / or the third list being exchanged between the first receiver and the second receiver,

[0033] (I) upon receipt of the third list and / or the first list, respectively, the first receiver and / or the second receiver establish a fifth list comprising the dates on which the first photons were received at the first receiver, for the pairs for which the two entangled photons were received at two receivers, since some photons may have been lost during transmission between the transmitter and one or both receivers,

[0034] (J) if only one of the two receivers establishes the fifth list, said fifth list being transmitted, preferably electronically signed, to the other receiver, then the first receiver and the second receiver respectively establish a sixth list and a seventh list of relative polarization states of the photons as received by the first receiver, the sixth list being derived from the second list and the fifth list, the seventh list being derived from the fourth list and the fifth list, each relative polarization state, on the sixth list, of a photon received at the first receiver at a time marked on the fifth list being the same relative polarization state as that of the corresponding photon received at the same time and marked on the second list, each relative polarization state, on the seventh list,of an entangled photon to a photon received at the second receiver at a time marked on the fifth list being the relative polarization state complementary to the polarization state of the corresponding photon received at the second receiver after the additional travel time La and marked on the fourth list, ,

[0035] (K) the respective signatures of the sixth list and the seventh list being exchanged between the first and second receivers to be compared according to a comparison method,

[0036] (L) if the signatures of the sixth list and the seventh list are identical, the list of deduction of information I is considered to be not listened to.

[0037] The relative polarization of a photon may be the polarization of the photon. Preferably, the relative polarization of a photon is a bit assigned to all possible polarizations that the second entangled photon may take after the first photon reaches the first receiver, where 1 is said bit assigned from an entangled photon to a photon to which a 0 has been assigned.

[0038] The comparison method in step (K) may comprise the steps of: i. mixing, at the first receiver, a first secret number, shared or to be shared with the second receiver, called a mixing number, with the sixth list, using a mixing function, in order to obtain a first mixed data item, ii. hashing, at the first receiver, the first mixed data using a hash function, iii. encrypt, at the first receiver, the hash of the first data mixed with a second secret number shared or to be shared with the second receiver, iv. send, to the first receiver, to the second receiver, the encrypted hash of the first data mixed with the second secret number, v. receive, at the second receiver, the data sent by the first receiver in step iv, vi. decrypting, at the second receiver, the received data, vii. mixing, by means of the second receiver, the first secret number with the seventh list, using a mixing function, in order to obtain a second mixed data, viii. hashing, at the second receiver, the second mixed data using a hash function, ix. compare, at the second receiver, the hash of the second mixed data with the decrypted received data.

[0039] The first secret number may be kept secret and used again. The first secret number may preferably be changed periodically, for example every time or every day.

[0040] The second secret number may be kept secret and reused or, preferably, may be changed periodically, for example every time or every day.

[0041] The first secret number may be a first renewable key, for example renewed after each use and / or the second secret number may be a second renewable key, for example renewed after each use.

[0042] Preferably, the first secret number is kept secret and reused, and the second secret number is a one-time key renewed after each use.

[0043] The transmission and detection method is preferably not implemented if the first or second key is no longer secret.

[0044] The receivers may share the secret numbers with each other before step (K) takes place. Alternatively, the secret numbers may be exchanged between the two receivers after step (K). The receivers may share the secret number by sending it to each other encrypted using a one-time key.

[0045] A mixer number identifier may be exchanged between the first and second receivers, each of which is capable of retrieving the corresponding mixer number from a stored list of mixer numbers.

[0046] The mixing function may be a logical XOR function, or a suffix function, consisting of adding the mixing number to the end of the sixth list, or an encryption function using the mixing number as an encryption key to encrypt the sixth list.

[0047] The mixing function may alternatively be a combination of an XOR function, a suffix function of adding the mixing number to the end of the first data set, and an encryption function using the mixing number as an encryption key to encrypt the first data set.

[0048] The encryption function may be an XOR function.

[0049] A signed message may be exchanged after step ix. between the two receivers before the sixth and seventh lists are used as one-time keys.

[0050] The deduction list of information I can be considered as not having been listened to if the two data compared in step ix. are equal.

[0051] The lists established in step (G) can be established for the transmission of a single information I. Alternatively, the lists established in step (G) can be established using transmitted photons for the transmission of a series of multiple information I.

[0052] The second propagation path is preferably physically protected against eavesdropping, at least for a portion of the second propagation path ending at the second receiver, where the photons propagate from the transmitter after their entangled photon has been received by the first receiver. This makes it possible to prevent a hacking device placed in this unprotected portion of the propagation path from being able to eavesdrop and retransmit the photons propagating there while they are no longer entangled. This portion is preferably long enough so that the difference between the travel time of a photon in said portion and the travel time of the photon in the non-entangled state towards the second receiver can be detected by the second receiver and such detection allows the second receiver to mark any incoming message as being potentially eavesdropped by a third party.

[0053] Two polarization rotators are preferably placed in front of the two photon receivers, respectively, the two photon rotators changing the polarization direction of the photons synchronously and randomly, for example by 45° or 0°, for example every photon or every other photon, so that a spy photon transmitter cannot know the polarization directions measured by the receivers. The two receivers can share a list of random bits, where 0 represents a 0° rotation and 1 a 45° rotation.

[0054] This prevents a known secret number from being generated by a hacker who would replace the entangled photon transmitter with a photon transmitter sending pairs of non-entangled photons representing a message that is also to be sent by the first receiver.

[0055] The sixth list and the seventh list may consist of bits, and may potentially be used as a shared list of random bits.

[0056] The transmitted message M can be used as an encryption key if the deduction list has been considered not to have been listened to.

[0057] The encryption keys generated during the transmission and detection process and / or consisting of the message M, can be used if the deduction list has been considered not to have been listened to, as first and / or second secret numbers.

[0058] The first receiver may encode the same information I on many successive incoming photons, since some of their entangled photons may be lost before reaching the second receiver.

[0059] The first receiver can reserve information Io to be used to separate the sending of any two other pieces of information, in particular if these two other pieces of information are identical, representing for example the same letter.

[0060] Step (F), consisting of deducing the transmitted message M from the deduction list, can be carried out by the first receiver having coded a separation letter between any two equal successive letters of the message M, taking into account the travel time ttta and the fifth list, by removing from the deduction list the photon polarizations for which the first entangled photon has never reached the first receiver, in order to create an approved deduction list, and the second receiver deducing the transmitted message M from the approved deduction list.

[0061] Alternatively, the second receiver may count as received information any information successively recorded on the deduction list more than a predefined number of times within a predefined number of successively received information I. For example, if there are 450 different polarization state pairs that can be encoded on the photons and if the propagation paths lose 90% of the photons between the transmitter and the receivers, the second receiver may count as received information any information appearing at least 6 times among the 200 received photons, or any information appearing at least 6 times among the 200 successive records of the deduction list.

[0062] Message M can be considered not to have been listened to if the deduction list was considered not to have been listened to.

[0063] The pair of complementary absorption polarizations may be selected from at least three different pairs of complementary absorption polarizations.

[0064] The pair of complementary absorption polarizations may be selected from at least 210 distinct pairs of complementary absorption polarizations.

[0065] A plurality of pairs of entangled photons can be generated successively by the transmitter, each pair of photons making it possible to transmit information from the first receiver to the second receiver. First quantum communication system

[0066] According to another of its aspects, the invention relates to a first quantum communication system implementing the method described above, comprising: - an emitter of entangled photons, comprising a source configured to generate at least one pair of entangled photons comprising a first photon emitted on a first propagation path, and simultaneously a second photon emitted on a second propagation path different from the first propagation path, - a first receiver arranged on the first propagation path, comprising a complex absorber configured to absorb the photon in a polarization state selected from the states of at least two different pairs of complementary polarization states, - a second receiver arranged on the second propagation path so as to be reached by the second photon after the first photon has reached the first receiver, said second receiver comprising: • an optical amplifier allowing the second photon to be multiplied while maintaining its polarization, and • placed downstream of the amplifier, a measuring instrument allowing the average polarization of the multiplied photons to be measured.

[0067] The complex absorber may be configured to absorb the photon in a state of predetermined polarization selected from the states of at least three different pairs of complementary polarizations.

[0068] The complex absorber may comprise: - at least one instrument capable of absorbing the photon in one or other of two complementary polarization states, - a polarization modifier which is disposed upstream of said instrument and is configured to convert the polarization of the first photon into the selected polarization according to which said instrument absorbs the photons.

[0069] The polarization modifier may comprise a polarization direction modifier disposed upstream of a polarization phase modifier.

[0070] The polarization direction modifier may comprise two quarter-wave plates arranged one after the other on the propagation path of the first photon, the orientation of at least one of the two plates being variable.

[0071] The polarization direction modifier may comprise a blade or prism of chiral or rotating material inducing a rotation of the polarization by an angle depending on the location through which the wave enters said chiral or rotating material.

[0072] The polarization phase modifier may comprise a first plate or a first birefringent prism dividing the beam into two electromagnetic waves of linear polarization, one along a first axis and the other along a second axis, and a plate with variable refractive index retardation arranged on the second axis.

[0073] Said at least one instrument may comprise at least one filter making it possible to send the first photon to one or the other of two photon detectors depending on the polarization state of the first photon.

[0074] The measuring instrument of the second receiver may comprise at least one detector of photons arranged to measure the polarization of the light resulting from the multiplication of the second photon.

[0075] The measuring instrument of the second receiver may comprise a succession of semi-reflecting plates arranged downstream of the optical amplifier, said plates directing the flux of photons multiplied with equal intensity towards a first phase measuring instrument, this being a polarization measuring instrument arranged to measure the intensity of the flux along two perpendicular axes, a second phase measuring instrument measuring the phase shift of the light between these same two axes, and a third phase measuring instrument measuring the phase shift of the light between the bisector of the same axes and an axis perpendicular to this bisector.

[0076] The first semi-reflecting plate can deflect one third of the luminous flux towards the first phase measuring instrument, and the second semi-reflecting plate can deflect half of its incoming luminous flux towards the second phase measuring instrument and the remaining half of its incoming luminous flux towards the third phase measuring instrument.

[0077] The optical amplifier may be a doped fiber amplifier.

[0078] The transmitter may be configured to successively generate a plurality of pairs of entangled photons.

[0079] The transmitter and each of the receivers may comprise a clock, the clocks of the transmitter and the receivers being synchronized with each other.

[0080] The second receiver may comprise a switch arranged in front of the optical amplifier and configured to absorb or reflect the photon(s) subsequent to a first photon reaching said second receiver within a predetermined time interval.

[0081] The first quantum communication system may comprise a second transmitter capable of generating one or more pairs of entangled photons, the second transmitter being located closer to the second receiver than to the first receiver. Second quantum communication system

[0082] The invention also relates to a second variant of a quantum communication system according to the invention, comprising: • an emitter of entangled photons, comprising a source configured to generate at least one pair of entangled photons comprising a first photon emitted on a first propagation path, and simultaneously a second photon emitted on a second propagation path different from the first propagation path; • a first receiver arranged on the first propagation path, comprising a complex absorber configured to absorb the photon in a polarization state selected from the states of at least two different pairs of complementary polarization states, except for exactly two pairs of perpendicular linear polarizations, the polarizations of one of the pairs being at 45° to the polarization directions of the other pair; • a second receiver arranged on the second propagation path so as to be reached by the second photon after the first photon has reached the first receiver, said second receiver comprising: - an optical amplifier allowing the second photon to be multiplied while maintaining its polarization and, - placed downstream of the amplifier, a measuring instrument allowing the average polarization of the multiplied photons to be measured.

[0083] The second variant of the system according to the invention is arranged to retransmit almost instantaneously a series of values, continuous or discrete, between two locations.

[0084] The first and second photons being entangled, the absorption of the first photon at the first receiver instantly determines the polarization of the second photon, in particular before it reaches the second receiver.

[0085] Measuring the average polarization of the photons multiplied at the second receiver then makes it possible to detect in which polarization state the first photon was absorbed and to deduce the information transmitted.

[0086] This second variant of the system therefore makes it possible to transmit information without latency, regardless of the distance between the two places wishing to communicate, and using only photons, which requires little energy.

[0087] The second variant of the system is for example used for communication networks and computer networks on Earth, in the sky and / or in space, in particular for communicating with systems far from Earth, such as satellites or spacecraft. Jones's Polarizations

[0088] By "complementary polarization states", also referred to hereinafter as "complementary absorption polarization states", is meant two polarization states of a light for which the modification of the polarization of said light by linear optical elements, in particular mirrors, birefringent plates and / or prisms, including quarter-wave plates, allows for one its absorption by a first polarizing filter, and for the other its absorption by a second polarizing filter according to a polarization orthogonal to that according to which the first polarizing filter can absorb.

[0089] In the following, the terms "state of polarization" and "polarization" are used interchangeably.

[0090] The first receiver is advantageously arranged so that its user can select the polarization state in which the photon is absorbed from any one of the possible polarizations as defined by the Jones formalism, in particular from a set of elliptical polarizations (also called "ellipsoidal") characterized by the orientation and the ellipse of the polarization.

[0091] It is thus possible to vary the polarization according to which the photons are absorbed by the first receiver in order to transmit a series of information to the second receiver.

[0092] By selecting, for example, 10 different polarization directions, for example spaced 9° apart from each other, and 21 different phase shifts, also spaced 9° apart from each other, it is possible to define 210 different polarization states and thus transmit 210 different signals.

[0093] For example, it is possible to transmit the letters of the alphabet in upper case, in lower case, numbers and a certain number of other special characters, for each of the pairs of entangled photons reaching the receivers. Complex absorber

[0094] A "complex absorber" is a set reached by the first photon making it possible to determine a pair of complementary polarizations from among a certain number of pairs of complementary polarizations, and to absorb the first photon in one of the two polarization states of the predetermined pair.

[0095] Preferably, the complex absorber of the first receiver is configured to absorb the photon in a state of a predetermined pair of complementary polarizations, selected from the states of at least three different pairs of complementary polarizations, and preferably from a number of different pairs of complementary polarizations selected according to the number of different values ​​to be transmitted, as described above.

[0096] Preferably, the complex absorber comprises: - at least one absorption instrument capable of absorbing the photon in one or other of two states of a pair of complementary polarizations, for example two orthogonal linear polarizations; - a polarization modifier disposed upstream of said absorption instrument and configured to transform the polarization of the first photon into the selected polarization according to which said absorption instrument absorbs the photons.

[0097] By "selected polarization" is meant a pair of complementary polarizations predetermined according to the information to be transmitted. Polarization modifier

[0098] The linear polarization of a photon can be converted into ellipsoidal polarization as represented by the Jones formalism by firstly modifying the orientation of the polarization of a photon of linear polarization and known direction, thus distributing in a predetermined manner the electric field along an x ​​axis and a y axis perpendicular to the x axis and then, in a second step, by modifying the phase of the electric field along one of two perpendicular directions, for example the y axis-

[0099] The polarization modifier preferably comprises a polarization direction modifier disposed upstream of a polarization phase modifier.

[0100] For example, if 0 is the rotation angle of the linear polarization and ÿ the phase shift along the y axis, being the pulsation of the wave, the components Ex and Ey of the electric field after the rotation are:

[0101] EX = E Cos (3) Cos (œt)

[0102] Ey = E Sin (0) Cos (œt)

[0103] And after the phase shift:

[0104] Ex = E Cos (0) Cos (Ml)

[0105] Ey = E Sin (3) Cos (art + ¢) Polarization direction modifier

[0106] A linear polarization direction can be modified in different ways, for example by a half-wave plate or alternatively by a double quarter-wave plate.

[0107] The polarization direction modifier may comprise two quarter-wave plates arranged one after the other on the propagation path of the first photon, the orientation of at least one of the two plates being variable.

[0108] The first quarter-wave plate modifies, for example, the linear polarization into circular polarization and the second quarter-wave plate converts, for example, the circular polarization into a linear polarization whose direction is oriented along an axis dependent on the direction of the axis of the second quarter-wave plate.

[0109] A rotation of the axis of this second blade therefore makes it possible to modify the direction of the linear polarization of the photon. If the blade is a half-wave blade, the rotation of this so-called half-wave blade makes it possible to modify the direction of the linear polarization of the photon.

[0110] Alternatively, the orientation of the first quarter-wave plate can be modified, that of the second being fixed, or the orientations of the two quarter-wave plates can be modified.

[0111] The rotation of a quarter-wave plate or a half-wave plate is obtained for example by mechanical control to a sensor or to an electronically controlled device. electrically allowing its rotation, for example by rubbing on a shaft set in motion by a piezoelectric material or by an electric motor device, for example direct current.

[0112] Alternatively, a plurality of linear polarization rotation devices may be used, each allowing different rotation angles, for example fixed, but which may just as easily be modifiable, selectors making it possible to send the photons to one of these rotation devices and, at the output of said rotation device, to conduct said photon to a common waveguide or a common transmission axis.

[0113] These selectors may comprise a mirror whose axis direction is controlled for example by an electrical device, or alternatively made up of a prism or a blade made of a material whose refractive index depends on an electric field: a Pockels cell, or a transparent material with a non-linear refractive index, another light flux, for example transverse and preferably of a wavelength different from that of the photon and not being able to generate photons having the same wavelength as that of the photon, varying the refractive index of said non-linear material and thus controlling the location and optionally the direction of exit of the photon from said material.Since the rotational inertia of a quarter-wave plate can be significant, the photons can be sent successively towards different quarter-wave plates whose direction will have been adjusted beforehand, for example by one of the mechanical rotation devices described previously, thus allowing time to modify the direction of each of these quarter-wave plates between two photon passages.

[0114] Alternatively, chiral or rotatable materials may be used to modify a linear polarization direction.

[0115] The polarization direction modifier may comprise a blade or prism made of chiral or rotating material inducing a rotation of the polarization by an angle depending on the location through which the wave enters said chiral or rotating material. The material may in particular be arranged between two Pockels cells.

[0116] The first photon may be projected onto a first plate or a first prism forming a Pockels cell whose refractive index is controlled by an electric field to emerge therefrom in different places, in particular onto an intermediate plate or prism made of at least partly chiral or rotating material rotating the electric polarization axis of the photon by an angle depending on the place through which the wave enters said intermediate plate or prism, before entering a second plate or a second prism forming a Pockels cell whose refractive index is adjusted symmetrically with respect to that of the first plate or the first prism to cause the photon to emerge in the same direction as if the refractive indices of the first plate or prism and the second plate or prism both had a fixed value. A third plate whose refractive index can be adjusted, for example electrically, is advantageously placed after the second plate or prism to make the location of the photon exit from the set of plates and prisms independent of the refractive index selected for the first plate or prism.

[0117] The blade or prism made of intermediate material is for example composed of two symmetrical prisms joined together with the same refractive index but having different chiral or rotary powers, the first of the two prisms having for example a chiral or rotary power and the second not having one or else rotating the electric field in the opposite direction to the rotation imposed by the first prism.

[0118] One of the two intermediate prisms may comprise a chiral material, for example cadmium selenide (CdSe) nanoparticles having a diameter of about 1.4 to 2.4 nm as described in the article by Visheratina, Anastasia, and Nicholas A. Kotov. "Inorganic nanostructures with strong chiroptical activity." (CCS Chemistry 2.3 (2020): 583-604.); the other intermediate prism preferably not being chiral or alternatively being of inverse chirality to that of said first intermediate prism. The rotation of the electric field of the waves passing through a chiral material being proportional to the thickness passing through said chiral material, the rotation of the electric field passing through the intermediate plate depends on the location through which it is penetrated by the light passing through it.

[0119] One of the two intermediate prisms may also comprise a "rotating" material, such as a superposition of an even number of quarter-wave plates stacked on top of each other in directions incremented at each layer by a predetermined angle, such that a wave linearly polarized along the axis of the first slice of the material emerges from the stack with a polarization rotated by an angle proportional to the thickness of the stack. Polarization phase modifier

[0120] A second device, called a "polarization phase modifier", can be arranged downstream of the polarization direction modifier, in order to phase shift by a predetermined angle the component of the electric field of the photon along one of two fixed axes.

[0121] Preferably, the polarization phase modifier comprises a first birefringent plate or prism arranged to divide the beam into two electromagnetic waves of linear polarization, one along a first axis, the other along a second axis, and a delay plate having a variable refractive index arranged on the second axis.

[0122] By "beam" we must understand the light wave that is the first photon in the sense of the duality of light.

[0123] The delay plate causes the wave oriented along the second axis to acquire a predetermined phase shift relative to the wave oriented along the first axis, before being mixed with it again by a new plate or a new birefringent prism making it possible to bring together along the same axis the two waves whose polarization fields are perpendicular.

[0124] The delay plate may comprise a Pockels cell or a non-linear material. The variable refractive index makes it possible to select the phase shift imposed on the wave oriented along the second axis.

[0125] In a first exemplary implementation, as described above, the phase modifier rotates a linear polarization of angles spaced 9° apart varying between -45° and +36° and varies the phase of angles spaced 9° apart between -90° and +90°, thus defining 210 possible polarization states. As described below, 209 of the 210 possible polarizations are for example used to encode data and the 210th linear polarization is used to absorb any entangled photon received within a predetermined time after the reception of a photon having been used to encode data.

[0126] In a second exemplary implementation, the phase modifier rotates the polarization axis by 45° before the photon is absorbed to transmit, for example, a 0, and transforms the polarization of the photon into circular polarization to transmit, for example, a 1. Reflection of the first photon

[0127] The invention also relates to a third variant of the quantum communication system according to the invention, comprising: • an emitter of entangled photons comprising a source configured to generate at least one pair of entangled photons comprising a first photon emitted on a first propagation path, and simultaneously a second photon emitted on a second propagation path different from the first propagation path; • a first receiver arranged on the first propagation path, comprising: - at least one first absorption instrument, arranged to absorb the first photon in one of two states of a pair of complementary polarizations, the polarization being undetermined in the observable basis according to which the first instrument absorbs the photons, - an optical selector arranged upstream of said at least one first instrument and configured to either allow the first photon to pass towards said at least one first measuring instrument, or prevent it from being measured; • a second receiver arranged on the second propagation path so as to be reached by the second photon after the first photon has reached the optical selector and / or after it has been able to reach the measuring instrument of the first receiver, said second receiver comprising an optical amplifier making it possible to demultiply the second photon while maintaining its polarization and, arranged downstream of the amplifier, a measuring instrument making it possible to measure the average quantum state of the demultiplied photons.

[0128] By "observable basis" we mean a basis of two complementary polarizations, for example two orthogonal linear polarizations.

[0129] By "undetermined polarization in an observable basis" is meant a photon whose polarization as observed in one of the two predetermined polarizations of an observable basis is not defined, that is to say is random, for example in an equiprobable manner.

[0130] The first and second photons being entangled, the absorption of the first photon at the first receiver instantly determines the polarization of the second photon, in particular before it reaches the second receiver.

[0131] Measuring the polarization of the photons multiplied at the second receiver then makes it possible to detect whether or not the first photon has been absorbed, and to deduce what information has been transmitted. The information transmitted by this third variant of the system is, for example, of the binary type.

[0132] The first receiver may comprise at least one second absorption instrument, the optical selector being arranged upstream of the first and second instruments and configured to either allow the first photon to pass by directing it towards one or other of the instruments, or to prevent it from being absorbed.

[0133] The use of two instruments makes it possible to transmit three different pieces of information, for example the values ​​0, 1 and 2, the value 0 being for example assigned to the reflection, the value 1 to the first instrument, and the value 2 to the second instrument. Optical selector

[0134] The optical selector of the first receiver can be of various types. It is advantageously placed upstream of the measuring instrument in order to be able to prevent the incident photon from reaching the measuring instrument, if this is desired.

[0135] To do this, the selector preferably comprises a reflector, in particular a controlled mirror, making it possible, for example, to reflect the first photon on a propagation path different from its incident propagation path, in particular on a propagation path not comprising the measuring instrument.

[0136] By "controlled mirror" is meant a device of which certain properties, for example the refraction properties or the direction of reflection, are controlled by an ancillary device connected to the mirror, in particular an electronic device, for example generating an electric field.

[0137] The optical selector preferably comprises a device whose refractive index and / or reflection direction are controlled, in particular controlled by an electric field or a luminous flux.

[0138] Alternatively, the optical selector comprises, for example, a Bragg mirror, in particular a Bragg mirror whose direction of reflection is controlled by a piezoelectric material, itself controlled by an electric field.

[0139] As a variant, the optical selector comprises a prism, in particular comprising Pockels cells whose refractive index is controlled by an electric field, the application of an electric field being able to direct the photon towards the or one of the measuring instruments or towards a Bragg mirror advantageously inclined relative to the direction of incidence of the electromagnetic waves reaching it, such that said waves are reflected towards a location preferably different from that from which they come at the entrance of the prism.

[0140] In another variant, the optical selector comprises one or a succession of Bragg filters, certain layers of which are Pockels cells whose refractive index is controlled by an electric field, said Bragg filter reflecting or allowing light to pass depending on whether or not the electric field is applied.

[0141] Alternatively, the Pockels cells used above are replaced by non-linear crystals illuminated by a powerful light capable of varying the refractive index of the medium crossed by the photon, the wavelength of the powerful light preferably being different from the wavelength of the photon.

[0142] The optical selector makes it possible in particular to orient the photons in three different directions, one direction allowing for example the photons not to be detected, a second making it possible to measure a linear polarization of the photons and a third making it possible to measure a circular polarization. Protective device

[0143] Preferably, the quantum communication system according to the invention further comprises a device for protecting the quantum state of at least one photon, in particular a device which prevents the measurement or absorption of at least one photon, arranged close to the first receiver so as to make it possible to protect the quantum state of the first photon after its reflection, preventing it from being absorbed or measured by one or more measuring instruments, said quantum state of the first photon being protected at least until the second photon has been multiplied at the second receiver.

[0144] The quantum state protection device is placed near the first receiver so as to protect the quantum state of the first photon when it is reflected and / or deflected from its incident propagation path by the optical selector so as not to be there observed, that is to say when we do not want it to be absorbed by the measuring instrument of the first receiver.

[0145] Preferably, the quantum state protection device comprises a transparent space, in particular a transparent space and at least one mirror. The transparent space may be empty or filled with gas or liquid.

[0146] Preferably, it comprises a plurality of Bragg mirrors, arranged relative to the transparent space so as to trap the photon that it receives on a path of appropriate length, as described above, that is to say corresponding to the time it takes for the second photon having reached the second receiver to be amplified there.

[0147] Alternatively, the protection device comprises an optical fiber of a length allowing the first photon to circulate there while waiting for the second photon having reached the second receiver to be amplified there.

[0148] In another variant, the device may be a portion of space or atmosphere, empty or filled with gas, which is ensured not to be crossed by an object reflecting or absorbing light. First Photon Absorption Instrument

[0149] At the first receiver, the first photon may be absorbed by at least one absorption instrument in one of two states of a pair of complementary polarizations.

[0150] Preferably, the absorption instrument comprises at least one filter making it possible to send the first photon to at least one photon detector, in particular to one or the other of two photon detectors depending on the polarization state of the first photon, the filter preferably being a prism or a blade made of birefringent material.

[0151] The absorption instrument may also comprise a polarizing filter and a photon detector located after said polarizing filter.

[0152] The absorption instrument may further comprise a semi-transparent mirror reflecting circularly polarized photons to a first photon detector and passing others to a second photon detector, as described in the May article, Wending, et al. "Broadband transparent chiral mirrors: Design methodology and bandwidth analysis." (A1P Advances 9.4 (2019): 045305). Photon emission Photon pair emitter

[0153] Preferably, the transmitter generates pairs of entangled photons by spontaneous parametric frequency downconversion (SPDC), i.e. by a method in which an initial photon, also called a "pump" photon, is split and its frequency halved by a four-wave mixing phenomenon, in an optical medium of non-linear refractive index, as described in the article by Amanti et. al, “Integrated sources of entangled photons at the heart of quantum technologies” (Photoniques, issue 91, 2018).

[0154] This type of photon pair emitter makes it possible to produce photons whose entanglement is relatively robust, but has the disadvantage of sometimes producing more than one pair of photons at a time, which is not desirable because it is not controlled. Additional devices can be put in place to deal with these multiple "parasitic" pairs, as described below.

[0155] Alternatively, an emitter comprising a quantum dot can be used to generate pairs of entangled photons, as described in the aforementioned article, which makes it possible to obtain pairs more regularly. The entanglement properties of the photons obtained by such a method can nevertheless sometimes be unstable.

[0156] Birefringent crystal optical fibers can also be used, as described in the article by Smith et. al “Photon pair generation in birefringent optical fibers” (Optics Express, Vol. 17, Issue 26, 2009).

[0157] Preferably, the transmitter is configured to successively generate a plurality of pairs of entangled photons.

[0158] The entangled photons at the output of the transmitter can be sent on the first and second propagation paths in various ways. Emission according to a predetermined polarization

[0159] The photons are preferably emitted according to a predetermined polarization. By "predetermined polarization" is meant in one of the two states of a predetermined pair of complementary polarizations, for example a linear polarization of a certain direction. A birefringent plate can for example separate the two entangled photons according to their vertical or horizontal linear polarization.

[0160] A predetermined polarization of the entangled photons sent to each of the receivers makes it possible in particular to know the probability of a state according to a polarization or its complementary polarization for any selected pair of complementary polarizations.

[0161] It is thus possible to generate series of random bits upon reception of said photons by the receivers, said series being complementary to the two receivers, the polarization of a photon received at the second receiver being the polarization complementary to the polarization observed at the first receiver.

[0162] A predetermined polarization is also necessary when using quarter-wave plates at the first receiver to rotate the polarization direction of the first photon.

[0163] To emit photons according to a predetermined linear polarization, for example, a plate or a prism comprising an optically transparent birefringent material, for example lithium niobate or rutile, is placed at the output of the emitter. (TiO2), whose optical indices depend on the polarization axis of the light through which at least one of the two photons passes.

[0164] This photon then exits the prism at one of two different locations, depending on its linear polarization.

[0165] If the source of entangled photons emits the two photons in the same direction and along an axis perpendicular to the ordinary axis of the optically transparent birefringent material, the first photon is collected at the exit of the prism, at the place through which the electromagnetic waves whose electric field is parallel to the ordinary axis of the optically transparent birefringent material exit, to send it to the first receiver.

[0166] In the same way, the second outgoing photon is collected from the place where the electromagnetic waves whose field is perpendicular to the ordinary axis exit in order to send it to the second receiver.

[0167] In the case where the two entangled photons are generated from the emitter at different locations and / or in different directions, each of the two photons can be projected onto birefringent prisms in a direction perpendicular to the ordinary axis of each of the prisms and each photon can be redirected towards the receiver intended for it, the photons exiting from different locations of the prisms then preferably being lost or destroyed by projection onto an absorbent surface.

[0168] For example, for the first entangled photon, the one leaving a first birefringent plate or a first birefringent crystal with a linear polarization parallel to the first axis can be used, and as the second entangled photon, the one leaving with a linear polarization parallel to a first axis of the crystal used for the second plate or the second prism which will have been adjusted to allow the exit of the photons according to a predetermined polarization corresponding to the polarization of the entangled photons to the photons leaving the first birefringent plate or prism in a direction parallel to the first axis.

[0169] To facilitate the transport of said photons to the receivers, birefringent delay plates are preferably placed at the exit of the places from which the photons leave the prisms, converting the linear polarizations of said photons into circular polarization.

[0170] Another birefringent delay plate is then preferably placed at the input of each of the receivers to convert the circular polarizations of the photons into linear polarization, this conversion into linear polarization making it possible to precisely adjust the polarization axis. Photon transmission

[0171] Photons may be transmitted from transmitters to receivers through space, atmosphere, optical fiber, or a combination of these means.

[0172] Lenses may be used for the transmission of photons, in particular for transmission through space or the atmosphere. Where appropriate, anti-reflection layers are preferably provided on said lenses. The size of the lenses used is preferably adapted to the length of the spatial or atmospheric transmission of the photons.

[0173] Conjugate mirrors that reflect the emitted light back to the transmitter can be used to adjust the direction of emission of the conjugated photons for spatial or atmospheric transmission. A laser light transmitter can, for example, explore a space in order to detect the receiver, the receiver reflecting the emitted light back to it and the direction of the conjugated photons then being adjusted to be parallel or coincident with the direction of the light reflected by the conjugated mirrors.

[0174] The light emitted by the laser light emitter may be of wavelength close to the wavelength of the entangled photons and be introduced by a dichroic prism into the objective lens used by the photons.

[0175] Alternatively, if the wavelength is the same as that of the entangled photons, the light can be introduced by a birefringent prism when said photons are of linear polarization, the polarization of the light used for guidance then being perpendicular to the polarization of the entangled photons directed towards the same receiver. A Pockels cell upstream of the receivers can be used to guide the light towards the conjugate mirrors when the guide light arrives.

[0176] In another variant, the light waves used for aiming can be emitted parallel to the entangled photons but separated, for example, by a distance of a few centimeters to be reflected by the conjugate mirrors.

[0177] In another variant, it is possible not to use a conjugate mirror but nevertheless to aim at the receivers or targets close to them, the information according to which the targets are received being communicated by another means of communication, in particular by radio signal or by quantum transmission.

[0178] The area to be explored can be identified by cartographic recognition of the area in which said receivers are likely to be located.

[0179] The aforementioned phase modifier can also be used when the receivers are in relative rotation with respect to the transmitter, in particular due to the rotation of the Earth or the satellites, to allow the photons emitted in a fixed direction with respect to the transmitter to penetrate into each of the receivers with a fixed and determined direction with respect to the latter. Calibration procedures

[0180] The various media crossed by the photons from their place of emission to the two receivers can give rise to modifications of their phase which are not necessarily desired or planned.

[0181] Furthermore, these modifications may be different depending on whether the photons are directed towards the first or second receiver. Finally, these modifications may vary over time depending in particular on the weather or the temperature of the materials during their use.

[0182] The system according to the invention can be periodically calibrated by having the photons absorbed by the first receiver in polarizations belonging to predetermined pairs of complementary polarizations and by observing for each of these pairs one of the two possible polarizations in which the entangled photon is detected by the second receiver.

[0183] Thus, the invention also relates to a method for calibrating a system as defined above making it possible to determine the polarization state of a photon reaching the second receiver as a function of the polarization state in which its entangled photon was absorbed at the first receiver, method comprising the steps consisting of: - generating pairs of entangled photons from an emitter, the first photon of the pair being emitted towards a first receiver and the second photon of the pair being emitted simultaneously towards a second receiver, the first and second photons being entangled according to their polarization state, - absorb the first photons at the first receiver in a predetermined pair of polarizations, store which of the two possible polarizations each photon was absorbed in, and stop sending photons from the transmitter as soon as a predetermined number of each of the different polarizations have been observed, - at the second receiver, duplicate the second photons into streams of multiplied photons using an amplification device, each multiplied photon having retained the polarization state of the second photon, - measure the polarization states, i.e. the polarization directions and phase shifts of each flux of multiplied photons, and store these measurements as well as their reception times, - transmit the list of polarizations and reception times of the stored photons from the first receiver to the second receiver, - delete from the list of photons received at the second receiver the photons not corresponding to photons received at the first receiver and, similarly, delete from the list of photons received at the first detector the photons whose corresponding photon has not been received at the second receiver, and - calculate using on the one hand: knowledge of the polarization state of two photons detected in complementary polarizations at the first receiver and whose entangled photons have reached the second receiver, and

[0184]

[0185]

[0186]

[0187]

[0188]

[0189] on the other hand, knowledge of the polarization state of the corresponding entangled photons received at the second receiver, the Jones matrix making it possible to deduce from the polarization of the photons received at the first receiver the polarization of the photons received at the second receiver. The storage of states as well as the calculation of the Jones matrix are carried out by any suitable electronic device, for example a microcontroller. The Jones matrix thus calculated makes it possible to calculate the polarization of the second entangled photon received at the second receiver as a function of the absorption polarization of the first photon by the complex absorber located at the first receiver. A second calibration can be made, consisting of determining the probability for any photon arriving at the second receiver, whose entangled photon was absorbed during its transit to the first detector, of belonging to each range of pairs of complementary polarizations detectable or identifiable by the second receiver; the range of a P polarization being defined as the set of polarizations assimilated by the polarization measuring instrument as being of P polarization. Thus, the invention also relates to a method for calibrating a system as defined above, making it possible to determine the probability of losing a photon during its transit from the transmitter to the first receiver, consisting of: - configuring the complex absorber of the first receiver to absorb photons received at the first receiver in one of two complementary polarizations of a pair of absorption polarizations, - successively generating several pairs of entangled photons from an emitter, the first photon of the pair being emitted towards a first receiver and the second photon of the pair being emitted simultaneously towards a second receiver, the first and second photons being entangled according to their state of polarization, - count the number of photons received at the second receiver in each of the polarization ranges detectable by the second receiver other than one of the two polarization ranges of the entangled photons of the photons absorbed by the first detector. It is thus possible to detect ranges of polarizations in which the entangled photons of photons lost during transmission during their transit to the first detector arrive in priority, or in the most probable way, and thus preferably avoid using the corresponding absorption polarizations to transmit data from the first to the second receiver. We can also, by taking the quotient between the numbers of photons received at the second receiver according to one of the polarizations corresponding to one of two absorption polarizations at the first receiver, calculate a transmission ratio of the photons between the transmitter and the second receiver. Second receiver measuring instrument

[0190] The measuring instrument of the second receiver preferably comprises at least one photon detector arranged to measure the polarization of the light resulting from the multiplication of the second photon.

[0191] The measuring instrument of the second receiver comprises, for example, a succession of semi-reflecting blades arranged downstream of the optical amplifier, said blades directing the flux of multiplied photons, i.e. the luminous flux, with equal intensity towards polarization measuring instruments arranged, for example, to measure the intensity of the flux along two perpendicular axes and / or the phase shift of the light between these same two axes.

[0192] The light can also be directed towards various polarizing filters after passing through one or a succession of lenses which enlarge the section of the light beam, thus allowing a plurality of mirrors or lenses to direct portions of this light beam towards the various polarization measuring instruments.

[0193] The various polarization measuring instruments preferably make it possible to: • measure the intensity of the component of the electric field of the light along a first axis x, • measure the intensity of the electric field component of the light along a second y axis perpendicular to the first x axis, • measure the phase shift between the light along its x axis and the light along its y axis, • and, preferably, measure the phase shift between the light along its x' axis, bisector of x and y, and the light along its y' axis.

[0194] The measurement of the intensity of light along two perpendicular axes is done for example by the separation of the light along two perpendicular axes by a birefringent plate or prism followed by two light intensity sensors placed at the outputs of said plate or said prism. The measurement of the phase shift between two perpendicular components is done for example by the separation of the light along two perpendicular axes by a birefringent plate or prism followed, for the wave polarized along one of the two axes, by a rotation of this polarization axis by 90°, for example thanks to a rotating or chiral material or by the succession of two quarter-wave plates, then a joint projection through Young's slits of these two waves, one of which has undergone the rotation of its electric field, onto a screen, the interference of the two light sources drawing fringes whose positions depend on said phase shift. Optical amplifier

[0195] The term "optical amplifier" refers to a device making it possible to duplicate a photon introduced therein, in particular the second photon of a pair of entangled photons, while preserving its polarization state.

[0196] Preferably, the optical amplifier is a doped fiber amplifier.

[0197] For example, it is possible to use an erbium amplifier (EDFA), for example 4 m long, into which the photon to be amplified is introduced at the same time as an amplifying wave of shorter wavelength, which makes it possible to amplify the wave corresponding to the introduced photon, with gains which can be of the order of 37 db / m.

[0198] A doped fiber amplifier (DFA) using a dopant other than erbium can also be used.

[0199] Alternatively, the optical amplifier is for example a vertical cavity amplifier (VCSOA), or a semiconductor type amplifier (SOA). Anti-reflective layers

[0200] To avoid the loss of photons, anti-reflection layers are preferably provided at the interfaces between adjacent transparent media of different indexes crossed by the photons, as well as at the interfaces of prisms and birefringent plates crossed by photons, the anti-reflection layer preferably being adapted to the index or indices of the material and to the angle or angles of incidence and to the directions of polarization as well as to the wavelength of the photon which must cross it. Dichroic filters

[0201] The first and / or the second receiver preferably comprise one or more dichroic filters allowing only photons of a given wavelength to pass through, in particular a prism made of a transparent dispersive material, the filter(s) preferably being arranged in front of the measuring instrument(s), or in front of the optical selector for the first receiver, and this in particular if the refractive indices of the non-linear materials are modified by applying powerful light fluxes.

[0202] Assignment of photons to information with synchronized clocks

[0203] When the photons arrive at the second receiver, it is useful to be able to differentiate whether they must be assigned to the transmitted information, whether it is information transmitted several times or whether it is information that would not have been coded on a pair of entangled photons.

[0204] Indeed, photon emissions are sometimes irregular, and an SPDS type emitter as mentioned above can, for example, emit a double pair of photons without this being desired.

[0205] The transmitter and each of the receivers preferably comprise a clock, the clocks of the transmitter and the receivers being synchronized with each other.

[0206] This makes it possible, when combined with knowledge of the flight time of the photons between the transmitter and each of the receivers, to determine coding and reception periods, preferably repetitive, during which a photon can be coded at the first receiver for the coding periods and its entangled photon arrive at the second receiver during the reception periods.

[0207] If a plurality of photons are received during a reception period, the first receiver maintains an unchanged state until a time between, for example, one quarter of the non-emission time after the end of the reception period and half of the non-emission time before the next reception period.

[0208] The second receiver preferably records the bits received for each reception period. It then advantageously transmits to the first receiver from time to time, in particular if the device uses reflection to transmit a bit or a trit, for example every 3000 reception intervals, or every 100 reception intervals without photon, a list of the reception periods for which it has not received a photon, the transmitted photon having been lost or no photon having been emitted by the transmitter during this period, without the first transmitter knowing whether it has reflected photons during these same periods, in particular if the device does not have a photon detector.

[0209] The transmission of this list can be done by instant communication using the method according to the invention described below, or by a conventional means of communication. Upon receipt of this list, the first receiver then transmits the bits corresponding to these transmission periods, for which no photon has reached the second receiver.

[0210] Alternatively, the first receiver uses only the two different measuring instruments to transmit the information, one detecting linear polarizations, the other circular polarizations.

[0211] The first receiver then retransmits each bit while selecting the measuring instrument appropriate to the bit it wants to transmit for that transmission period, and preferably keeps the selector in the same state until the end of the transmission period for which it receives a photon, this allowing it to select the measuring instrument to be used for the transmission of the next bit.

[0212] The second receiver, by receiving the photons during the transmission periods, and if it receives any, measures for each transmission period their state of polarization and deduces the bit that it must add to the list of bits received.

[0213] If the transmission line between the transmitter and the first receiver has a certain opacity and can absorb a certain proportion of the photons passing through it, some photons may arrive at the second receiver during reception periods with random polarizations.

[0214] The second receiver can then be configured to recognize at least some of the photons arriving in a polarization state which cannot be that of an entangled photon absorbed or reflected at the first receiver. Clock shift

[0215] Preferably, the clocks of the system components, namely the transmitter and the two receivers, are configured to take into account the phenomenon of different flow of time in different locations, in particular the different altitudes of each of the components.

[0216] Synchronization of transmission periods between receivers

[0217] A method can be implemented allowing the first and second receivers to synchronize their clocks.

[0218] For example, when measuring a first photon, the first receiver notes using its own clock the time at which said photon struck the measuring instrument.

[0219] The noted time is subsequently transmitted to the second receiver as well as, preferably, the references of the transmission interval, in particular the time and optionally the duration during which the photon was expected.

[0220] The second receiver notes the reception time of the second photon in order to adjust its own clock so that the offset between the start of the transmission period and the time during which the first photon struck the measuring instrument of the first receiver is the same as the offset between the start of the reception period of the second photon at the second receiver and the time given by the clock for the reception of the second photon.

[0221] If the transmission lines between the transmitter and one or other of the receivers absorb certain photons, the transmitter can send photons in a predetermined number, or for a predetermined duration, and each of the two receivers can note the average reception time of each of the photons and then one of the receivers can communicate this said average time to the other receiver.

[0222] The average time can be calculated by determining the average of the reception times of each of the photons or only of the first and last photons received. The predetermined number of photons sent or the duration of their sending are preferably adjusted in particular as a function of the transmission / loss ratio of photons on each of the two paths between the transmitter and the receivers, and the average frequency of sending the photons.

[0223] Since the transit times of the photons between the transmitter and each of the receivers are different, the synchronization of the clocks between each of the receivers may be different depending on whether the information is transmitted in one direction or the other. Each of the receivers may then have a synchronization register used to increment or, on the contrary, subtract from the time of the clock of said receiver a period of time adjusted during synchronization, to deduce therefrom the time of a synchronized clock for the reception of information from the other receiver. Transmission between transmitter and receiver

[0224] A method can be implemented for synchronizing the periods of sending photons to the receivers and the periods of receiving them at the receivers, these periods being time intervals during which photons can leave the transmitter or reach the receiver.

[0225] To this end, the transmitter can emit a first brief light signal followed or preceded by other light signals composing a message, preferably signed by a digital signature indicating the precise time, on its clock, of sending the signal.

[0226] Upon receipt of said first light signal, the receiver notes the reception time then reads the signal sending time, determines the difference between the signal sending time and the start time of the photon transmission period, during which the signal was sent, or if it was sent outside a transmission period, the start of the previous transmission period, and does the same with the signal reception time and the start time of the reception period.

[0227] If the difference between the date of transmission of the signal and the start of the transmission period is greater than the difference between the date of reception and the start of the reception period, the receiver can advance the start of the transmission period, or vice versa in the opposite case.

[0228] The calibration is advantageously repeated several times and the results are averaged, this making it possible to adjust the clocks with a precision greater than the imprecision of the sending and receiving times of said light signals.

[0229] The wavelength used for the light signal is preferably the same as the wavelength of the entangled photons, so that it can be transmitted at the same speed as the entangled photons.

[0230] Assignment of photons to information without synchronized clock

[0231] As an alternative to synchronized clocks, the first receiver may comprise detector-transmitters and a waiting element, for example a reflector arranged to reflect the first photon with a predetermined polarization different from the polarizations detectable by the detector-transmitters, or even an element arranged to absorb the first photon in a predetermined polarization different from the polarizations of the detector-transmitters.

[0232] The polarizations of the detector-transmitters are preferably complementary, such that any photon directed towards an absorbing waiting element is absorbed.

[0233] The detector-transmitters are preferably arranged to detect the polarization of the photons in at least four different polarizations, these polarizations being grouped into complementary pairs so that any photon directed towards a detector-transmitter is thus detected and absorbed regardless of its initial polarization.

[0234] The detector-transmitter(s) of the first receiver are used to send the information by selecting the pair of detectors used.

[0235] Each photon received by the first receiver during a predetermined period, also referred to as a "rest period", after the reception of a photon used to send information, is sent to the waiting element, the duration of this predetermined period being preferably fixed and preferably greater than twice the inaccuracy of the clock of the receivers, and the start of this rest period being determined by the sensor or one of the two sensors absorbing the photon used to send the information.

[0236] The second receiver is preferably arranged to, on the one hand, • ignore photons paired with photons sent to the waiting element, on the other hand, • interpret two successive photons not paired with photons sent to the waiting element as successive bits if these are separated by at least the rest period, from which the imprecision of the receiver clock is subtracted, and finally, • interpret two photons received successively in a time, for example, less than or equal to three-quarters of the rest period as representing the same bit.

[0237] The second receiver can thus detect an error in the transmission of information if: two consecutive photons of different polarizations not paired with photons sent to the waiting element are received in a time less than the rest period less the inaccuracy of the receivers' clock.

[0238] This method has the advantage of not requiring the placement of a switch at the transmitter to restrict the emissions of entangled photons, nor clock synchronization.

[0239] The detector-transmitter(s) of the first receivers can also serve at the same time as a waiting element, in particular if the polarization in which they detect the photons is adjustable and can therefore be adjusted to the polarization used by the waiting element to absorb the photons. Anti-noise device

[0240] Optical amplifiers tend to emit photons in the opposite direction of the propagation signal, either during signal amplification or in the absence of a signal, after molecules or atoms in the amplifying medium have been excited by a pump signal.

[0241] The second receiver comprises, for example, a switch arranged in front of the optical amplifier, in order to limit the number of photons emitted by the amplifier towards the source of entangled photons of the device.

[0242] The switch of the second receiver is for example configured to absorb or reflect the photon(s) subsequent to a first photon reaching said second receiver in a predetermined time interval.

[0243] The switch of the second receiver can be connected to the measuring instrument of the second receiver, in order to no longer allow light to pass in one direction or the other from the arrival of a first photon and until the next photon is expected or a predetermined time before this moment, for example half of the rest period defined above.

[0244] Alternatively, the switch of the second receiver may only allow photons to pass during the periods when they are expected, in particular during the time intervals for processing the aforementioned photons.

[0245] Assignment of photons to information without synchronized clock using low transparency optical transmission means

[0246] Optical fibers, although transparent, do not transmit all the photons presented at their input. A loss of 0.20 dB per kilometer is common, for example losing 10 dB in 50 km or 90% of the photons.

[0247] The effect of the photons lost in transit between the transmitter and the first receiver is however different from the effect of the loss of the photons lost during their transit to the second receiver; the entangled photons of the photons lost between the transmitter and the first receiver can arrive at the second receiver with any polarization corresponding to the polarization of the entangled photon absorbed in the line going to the first receiver, whereas the loss of a photon in the line leading to the second receiver necessarily causes the disappearance of a photon potentially carrying information, that is to say whose entangled photon has reached the first receiver.

[0248] Furthermore, the polarizations of the photons arriving at the second receiver after their entangled photons have been absorbed in transit to the first receiver are not necessarily equally distributed among all possible observable polarizations.

[0249] For the transmission of information, we therefore preferably use pairs of complementary polarizations for which corresponding polarizations observed at the second receiver are the least numerous when the entangled photon of the photon detected at the second receiver has been absorbed during its transit to the first receiver.

[0250] The invention also relates to a method for calibrating a system as defined above, making it possible to determine two Jones matrices, one of which makes it possible to calculating the polarization of a photon arriving at the second receiver as a function of the polarization of a photon absorbed at the first receiver, wherein, preferably, the amount of different polarizations observable at the second receiver is greater than twice the inverse of the photon transmission ratio between the transmitter and the first receiver, the method comprising: - configuring the complex absorber of the first receiver to absorb photons received at the first receiver in one of two complementary polarizations of a pair of absorption polarizations, - successively generating several pairs of entangled photons from an emitter, the first photon of the pair being emitted towards a first receiver and the second photon of the pair being emitted simultaneously towards a second receiver, the first and second photons being entangled according to their state of polarization, - count for each polarization in which a photon is received at the second receiver the number of photons having reached said second receiver with this same polarization, - stop sending photons when a predetermined number of photons have been received at the second receiver, - determine the two polarizations in which the photons were received most often at the second receiver, these polarizations being considered as corresponding to the absorption polarizations of the photons at the first receiver, - calculate the two possible Jones matrices of polarization transformation allowing the polarization of a photon received at the second receiver to be deduced from the polarization of a photon received at the first receiver.

[0251] Recording the polarization of at least one photon received at the first receiver and that of its entangled photon received at the second receiver, the correspondence being made for example thanks to their respective reception times, also makes it possible to select, from the two calculated Jones matrices, the one which makes it possible to calculate the polarization of the photons received at the second receiver as a function of the polarization of their entangled photons possibly received at the first receiver.

[0252] The following method can also be used to transmit information from the first to the second receiver, the method comprising the steps of: - successively generating several pairs of entangled photons from a transmitter, the first photon of the pair being emitted towards a first receiver and the second photon of the pair being emitted simultaneously towards a second receiver, the first and second photons being entangled relative to their polarization state, - for each information to be transmitted, configuring the complex absorber of the first receiver to absorb a number NPT of transmission photons in a predetermined complementary polarization pair called "absorption polarization pair" corresponding to the information to be transmitted, then, if the next information to be transmitted is not already known or is identical to the information just transmitted, configuring the absorber in a polarization pair called "standby polarization pair" and, if said information is identical to the information just transmitted, counting at least NPT photons absorbed in this "standby polarization pair". - at the second receiver, counting, for each pair of complementary polarizations, the number of photons received in one of the two polarizations of said pairs of polarizations since the last possible reception of a signal. As soon as this counter exceeds for one of the pairs a predetermined NSP threshold number and the pair of complementary polarizations is different from that of the last signal received, considering the information corresponding to this pair of polarizations as being a new signal, and if this last information does not correspond to the waiting pair of polarizations, adding this information to the list of information received.

[0253] Alternatively, at the first receiver, the polarization absorber is systematically configured to absorb at least NPT photons in one of the two standby polarizations after sending any information.

[0254] For example, to transmit information, we will use: • transmission lines between the transmitter and each of the receivers presenting an attenuation of 10 dB, i.e. a loss of 90% of the photons, • transmission lines between the complex absorbers, configured to absorb photons in 450 pairs of complementary polarizations, these pairs representing 80% of the photons received at the second receiver during absorption of their entangled photons in their transits towards the first receiver, • we can choose 200 photons for NPT and 6 for NSP, which makes it possible to obtain, according to the inventor's calculations, a transmission error rate which would then be less than 1 in 10,000.

[0255] In another example, with an error rate of 97% corresponding to a signal attenuation of 15 dB, using 450 pairs of complementary polarizations, each polarization and phase shift being separated from each other by approximately 5°, the coding of 1200 photons at the first receiver (therefore NPT=1200), the threshold number NSP being set at 14, makes it possible to obtain, according to the inventor's calculations, an error rate of less than 1 for 150,000 if the resulting photons at the second receiver of photons absorbed during their transits to the first receiver are equally distributed over all observable polarizations.

[0256] Processing of pairs of photons sent simultaneously

[0257] The transmitter may sometimes send pairs of entangled photons very close to each other. The photon detectors located at the first receiver therefore preferably count the number of absorbed photons and not only the number of photon impacts on said first receiver. This counting may, for example, take into account the intensity of the electromagnetic wave incident on the photon detectors.

[0258] Groups of photons can thus arrive almost simultaneously at the second receiver, the latter being incapable of discriminating the polarizations of the photons from one another. Since the polarization detector can detect an average polarization of all the photons detected "simultaneously", the polarization of the groups of photons arriving simultaneously at the second receiver, i.e. whose generated light intensity is for example 50% greater than the intensity generated by a single photon, advantageously does not give rise to an incrementation of the counters of photons received in various polarizations. However, it may sometimes be the case that a plurality of photons reach the first receiver but that only one of their entangled photons reaches the second receiver, the latter then being counted. Device performance

[0259] The use of lossless or low-loss lines between the transmitter and the first receiver, for example allowing photons to pass through a vacuum, makes it possible to reduce or avoid photons received at the second receiver with random polarization.

[0260] Similarly, the use at the second receiver of precise measuring instruments making it possible either to increase the number of pairs of complementary polarizations, or to ignore a large number of photons with random polarizations can make it possible to: • increase the transmission distance of the photons, • increase the bit rate by reducing the number of NPT transmission photons.

[0261] An increased switching speed of the polarization of the complex absorber of the first receiver makes it possible to increase the sending frequency of the entangled photons sent by the transmitter.

[0262] Increased temporal precision of the polarization detectors of the second receiver, which makes it possible to discern the parasitism of various photons received very close in time to each other, also makes it possible to use a larger flux of entangled photons, but also to reduce the number of receptions of photons received "simultaneously", as described above.

[0263] This method has the advantage of not requiring the installation of a com mutator at the emitter to restrict the emissions of entangled photons, nor clock synchronization. Processing of photon return to the emitter

[0264] Photons are sometimes reflected back to the transmitter from the receivers. To prevent them from being reflected again by the transmitter to one of the receivers, the cavity or material in which the entangled photons are produced by wave mixing, the refractive index of which is non-linear, is preferably surrounded or covered with a material absorbing light having a wavelength equal to that of the entangled photons. Quantum communication processes

[0265] The invention also relates to a quantum communication method using the system defined above, comprising the steps consisting of: - generating a pair of entangled photons from a transmitter, the first photon of the pair being emitted towards a first receiver and the second photon of the pair being emitted simultaneously towards a second receiver, the first and second photons being entangled, the second receiver being located on the propagation path of the second photon further from the transmitter than the first receiver, such that it arrives there later, - modifying, by means of a polarization modifier, the polarization state of the first photon when it reaches the first receiver into a polarization state dependent on the information to be transmitted, the state being selected from at least two different pairs of complementary absorption polarizations, with the exception of exactly two pairs of perpendicular linear polarizations of which the polarization directions of one of the pairs are at 45° to the polarization directions of the other pair, - absorb, using an absorption instrument, the first photon in one of the two complementary polarizations of the selected pair, - at the second receiver, duplicate the second photon into a stream of multiplied photons using an amplification device, the light thus created having retained the polarization state of the second photon, - measure the average polarization state of the light flux and determine according to this measurement the polarization state of the first photon, in order to deduce the information transmitted by the first receiver.

[0266] The pair of complementary photons is preferably selected from at least three different pairs of complementary polarizations.

[0267] The pair of complementary polarizations is for example selected from 210 distinct pairs of absorption polarizations, in particular from polarizations spaced 9° apart in their polarization direction and 9° out of phase.

[0268] The invention also relates to a quantum communication method using the system defined above, comprising the steps consisting of: • generating a pair of entangled photons from a transmitter, the first photon of the pair being emitted towards a first receiver and the second photon of the pair being emitted simultaneously towards a second receiver, the first and second photons being entangled, the second receiver being located on the propagation path of the second photon further from the transmitter than the first receiver, such that it arrives there later, • select, depending on the information to be transmitted, whether or not to absorb the first photon in one of two pairs of complementary polarizations when it reaches the first receiver, using an optical selector directing, or not, said photon towards an instrument or towards a plurality of instruments, • in the case where the selection leads to not absorbing the photon in a predefined polarization, trapping said first photon in a protection device making it possible to avoid its absorption at least until the second photon has reached the second receiver, • at the second receiver, duplicate the second photon into a stream of multiplied photons using an amplification device, each multiplied photon having retained the quantum state of the second photon, • measure the average quantum state of the flux of multiplied photons and determine according to this measurement whether the first photon was absorbed at the first receiver, and / or with which instrument, in order to deduce the information transmitted by the first receiver.

[0269] Preferably, the polarization of the pair of entangled photons is undetermined in the polarization(s) of the pair of complementary polarizations in which the instruments of the first receiver absorb them.

[0270] The pair of entangled photons reaches, for example, the receivers with a linear entangled polarization, one of the two complementary absorption polarizations being circular, the second receiver being arranged to distinguish whether the average polarization of the flux of demultiplied photons is circular or linear, and to determine according to this distinction whether the first photon has been measured or not.

[0271] Alternatively, the pair of entangled photons reaches the receivers with a circular entangled polarization, the quantum state of absorption of the photons being a linear polarization, the second receiver being arranged to distinguish whether the average polarization of the flux of demultiplied photons is circular or linear, and determine according to this distinction whether the first photon has been measured or not.

[0272] Alternatively, the pair of entangled photons reaches the receivers with a polarization linear vertical or horizontal, the quantum state measured at the first receiver being a linear polarization at 45° or -45° from the vertical or horizontal, the second receiver being arranged to distinguish whether the average linear polarization of the flux of demultiplied photons (P20) is at 45 or -45°, or vertical or horizontal, and determine according to this distinction whether the first photon has been measured or not. Transmission of information

[0273] The system according to the invention and the quantum communication method described above make it possible to transmit between the first and second receiver information either of the binary type, in the form of bits, or discrete or continuous values.

[0274] Preferably, several pairs of entangled photons are generated successively by the transmitter, each pair of photons allowing the transmission of information, for example of binary type, from the first receiver to the second receiver.

[0275] For example, one can choose to absorb the first photon at the first receiver to transmit a bit 1 and reflect it to transmit a bit 0. The measurement at the second receiver of the average quantum state of the flux of demultiplied photons then makes it possible to determine whether a bit 1 or a bit 0 is transmitted from the first receiver almost instantaneously.

[0276] Several methods can be implemented in order to secure the communication and avoid transmission errors, due for example to double pairs of photons emitted simultaneously.

[0277] For example, during time intervals previously established using the clocks described above, only the first photon reaching a receiver is preferably considered, the following photons being ignored.

[0278] As described above, photons may be counted as they arrive at a polarization detector. If the counting reveals the arrival of more than one photon during a predefined time interval, the bit is not transmitted during this interval, and is for example transmitted in the next time interval or, preferably, the same bit is retransmitted again.

[0279] At the second receiver, counting the photons arriving in the time interval where they are expected can advantageously make it possible to create a temporary list of unreceived bits. Two-way communication

[0280] To enable two-way communication, i.e. to enable each of the two receivers to transmit information to the other receiver, a plurality of transmitters can be used.

[0281] The system according to the invention may in particular comprise a second transmitter capable of generating one or more pairs of entangled photons, the second emitter being located closer to the second receiver than to the first receiver.

[0282] Alternatively, at least some of the photons can be made to travel an indirect path so as to lengthen their transport time to one of the receivers, for example by making the photons reflect on one or more intermediate mirrors, or by making them pass through media having high refractive indices, or by transporting them in optical fibers of varying lengths.

[0283] This elongated path can for example alternate at a fixed or variable rate depending on the needs, with the non-elongated path so as to be able to use the entangled photons sometimes to transmit the information from one point to another, sometimes in the other direction. Optical switches upstream of the receivers and synchronized with the switch affixed to the transmitter capable of sending the photons on an extended path, can be installed to send said photons to receivers corresponding to the first type of receiver, as described above, or on the contrary to the second type of receiver.

[0284] Method of transmitting a key and verifying that this transmission has not been listened to.

[0285] It is possible to verify that information transmitted by a flow of photons from the transmitter to the second receiver has not been listened to by implementing the following steps: - the second receiver establishes a first list of the dates of reception of the photons having conveyed the information as well as the relative polarization designating that of the two complementary polarizations in which each photon was received; - the second receiver generates a message containing the list collected in the previous step, creates an electronic signature of this list and transmits said list as well as the signature to the receiver; - the first receiver receives the list and the signature and then verifies said signature; - the first receiver establishes a second list consisting of the elements of the first list whose relative polarizations of the photons received by the first and second receivers are equal, or whose entangled photon has never reached the first receiver, two entangled photons having different relative polarizations; - if the number of elements of the second list restricted to pairs of entangled photons of which each of the two photons has reached their respective receivers is less than the product of a predetermined ratio by the count of the elements of the first list restricted to pairs of entangled photons of which each of the two photons has reached their respective receivers, then the information is declared to have been transmitted unheard.

[0286]

[0287]

[0288]

[0289]

[0290]

[0291]

[0292] We can then have the following steps: - if the information is declared to have been transmitted unheard, then the second list is sent signed by the first receiver to the second receiver, then a third list is created by the first receiver, consisting of the relative polarizations of the photons appearing in the first list and not appearing in the second list, - upon receipt of the second list by the second receiver and after verification of the signature, the third list is recreated in the second receiver using the first and second lists, then a signed message, confirming the correct receipt of the second list, is sent by the second receiver to the first receiver; and - the second receiver uses the third list as a shared key with the first receiver, and upon receipt by the first receiver of the message transmitted by the second receiver in the previous step, the first receiver uses the third list as a shared key in exchanges with the second receiver. A polarizing filter can be placed upstream of the second receiver. Method for comparing a first data set and a second data set The invention also relates to a method, implemented by at least one device, for comparing a first data set and a second data set, in particular with a view to determining whether these two data sets are identical, this method comprising the steps of: a. mix a number, called a mixer number, with the first data set, using a mixing function, in order to obtain mixed data, b. hash the mixed data using a hash function, and c. compare the hash thus obtained in step b) with a third data set assumed to be the hash of the second data set mixed with the same mixer number as used in step a) and using the same mixing function. Thanks to the invention, and in particular to the mixing of the first data set with a mixer number before hashing, it becomes very unlikely to be able to create data similar to this first data set which, after being mixed with the same mixer number, will have the same hash as the first mixed data set. Preferably, the method according to the invention does not require the simultaneous presence of two sets of data in the device. Preferably, the mixing number is randomly generated.

[0293] The mixer number is preferably generated by the device. Alternatively, the mixer number is generated by another trusted device.

[0294] The generation of the mixing number may be based on a pair of input values ​​that are physical quantities of which at least one varies continuously, such as temperature and time, or a quantum phenomenon. For example, such generation may be based on which of the two Young's slits a photon chooses to use to pass through a plate.

[0295] Preferably, the mixing operation of step a) is performed by the apparatus. Alternatively, the mixing is performed by another trusted apparatus.

[0296] The mixing function combines the first data set and the mixing number. It is preferably a logical XOR function that adds the bits of the first data set to those of the mixing number, one by one. Since the size of the mixing number is generally smaller than the size of the first data set, it is possible to add by means of an XOR the bits of the mixing number to the first or last bits of the first data set.

[0297] The mixing number can have the same size as the first data set. In this case, the addition using the XOR function is performed on all bits, one by one.

[0298] Alternatively, the mixing function is a suffix function consisting of adding the mixing number to the end of the first data set.

[0299] The mixing function can even be an encryption function using the mixing number as an encryption key to encrypt the first data set.

[0300] In one embodiment, the mixing function is a combination of an XOR function, a suffix function of adding the mixing number to the end of the first data set, and an encryption function using the mixing number as an encryption key to encrypt the first data set.

[0301] Preferably, the data of step b) is hashed by the device. Alternatively, the hashing is performed by another trusted device.

[0302] Preferably, the hash function is chosen from SHA1, SHA2, SHA256 and MD5 and the Jenkins function.

[0303] First method for verifying the integrity of a message

[0304] A first variant of the method according to the invention is a method making it possible to verify by means of the apparatus the integrity of a message coming from a sender, the method comprising the steps consisting of: i. receive, by means of the device, the message and a message identifier, said message forming the first data set, ii. generate the mixing number, iii. implement steps a) and b), in which the message is mixed with the number mixer then chopped, iv. optionally encrypt the mixing number, v. send, by means of the device, the message identifier and the optionally encrypted mixer number to the sender of the message, vi. receive, by means of the device, the third set of encrypted data, preferably with the message identifier, from the sender, vii. decrypt the third data set, and viii. implementing step c), the integrity of the message being ensured if the third data set decrypted in step vii and the hash obtained in step b) are identical.

[0305] By "integrity" of the message, we mean its non-alteration, for example by a malicious third party who intercepted it during its transmission.

[0306] The message identifier may be a sequence of alphanumeric characters and / or signs that can be converted into a digital word by means of, among other things, an ASCII code.

[0307] The message identifier may contain the sender's identifier and a message sequence number.

[0308] The authentication of the sender is notably ensured by the decryption operation carried out in step vii.

[0309] Decryption can be performed using an encryption key kept secret between the device and the sender.

[0310] Preferably, the mixing number is kept secret and a renewable key having the size of the hash (third data set) is used, in particular with an XOR as an encryption function.

[0311] Another solution is to keep the mixing number secret and use a non-renewed symmetric key with a symmetric encryption function.

[0312] Alternatively, the mixer number is kept secret and a non-renewed asymmetric key pair with an asymmetric encryption function is used.

[0313] Alternatively, the mixer number is kept secret and a non-renewed symmetric key with a symmetric encryption function is used.

[0314] Alternatively, the mixing number is a renewable key and another renewable key having the size of the hash (third data set) is used, notably with an XOR as an encryption function.

[0315] Alternatively, the mixing number is a renewable key and a non-renewable key having the size of the hash (third data set) is used, notably with an XOR as an encryption function.

[0316] Alternatively, the mixing number is a renewable key and a non-renewed symmetric key with a symmetric encryption function is used.

[0317] Alternatively, the mixing number is a renewable key and a non-renewed asymmetric key is used with an asymmetric encryption function.

[0318] Preferably, the mixer number identifier is exchanged between the sender and the device, each of which can retrieve the corresponding mixer number from a stored list of mixer numbers.

[0319] In another exemplary embodiment, the mixer number is randomly generated after each use. This mixer number may be encrypted by a one-time key. The mixer number may also be encrypted by a symmetric or asymmetric function.

[0320] This first variant of the invention makes it possible to ensure both the integrity of the message received and the identity of the sender of the message.

[0321] The steps relating to sending and receiving data may be carried out using the same communication protocol or different communication protocols. For example, the data received in step i is received by Wi-Fi, the data sent in step v is sent by 4G and the data received in step vi is received by WiMAX.

[0322] In step i, the device may also receive an identifier from the sender. This identifier is useful if the device is likely to receive messages from various senders, such an identifier allowing it to choose the encryption keys to be used to encrypt or decrypt the information exchanged with the sender during the encryption and decryption operations described in this first variant of the invention.

[0323] Preferably, the method according to this first variant comprises, between steps v and vi, the steps consisting of: - receive, from the sender, the message identifier and the optionally encrypted mixer number, - optionally decrypt the mixing number, - identify, using the message identifier, the message sent to the device, - mix the message with the optionally decrypted mixer number to using the blend function, - hash the data resulting from the previous step using the hash function, - encrypt the hash resulting from the previous step, and - send the encrypted hash to the device, preferably with the message ID.

[0324] The optional encryption of the mixer number in step iv is preferably performed by the apparatus.

[0325] Optional encryption of the mixer number prevents this number from being intercepted and modified by a malicious third party.

[0326] Preferably, the optional encryption of the mixing number is performed using a one-time key of size at least equal to that of the number. Since the key is one-time use, a new key is used each time a mixing number is sent.

[0327] Encryption can also be performed using a symmetric key. The symmetric encryption key is kept secret between the sender and the device and is preferably renewed after a certain number of transmissions.

[0328] Alternatively, the optional encryption of the mixing number is asymmetric, and is performed either using a public key of the sender known to the device, so as to allow decryption by the sender using its associated private key, or using a private key of the device whose public key is known to the sender.

[0329] This prevents a third party from knowing or modifying the mixing number.

[0330] Preferably, the decryption of step vii is performed by the apparatus.

[0331] The decryption of step vii can be performed using a symmetric key, if the encryption in step iv is performed using a one-time key.

[0332] Alternatively, the decryption of step vii is performed using a one-time key if the encryption of step iv is performed using a symmetric key.

[0333] The decryption of step vii can also be carried out by other methods, for example using a public key known to the device, associated with a private key of the sender used for the encryption of the hash received in step vi. The device is thus able to certify the identity of the sender.

[0334] The mixing number may have the same size as the symmetric key used for encryption, if such a symmetric key is used, and also the same size as the hash.

[0335] Preferably, the private, symmetric, single-use encryption keys and the mixing numbers are undetectable and unobservable by third-party devices, in order to prevent eavesdropping on the data sent by the sender or the device from generating and transmitting second fraudulent data sets that would cause the integrity of messages received by the device but transmitted by a sender other than the one supposed to legitimately hold said keys to be recognized in an erroneous manner.

[0336] If the encryption key X of the mixing number x is known, then the hash of the mixed message can be known, because it is sufficient to decrypt the encryption of x and to calculate the mixing of the message before hashing the latter. One can then also guess the key Y encrypting the hash or know that it belongs to a small universe, the hash of the mixed message and its encryption with Y being both known or observable. The encryption key Y is therefore a function F of the encryption key X, or the encryption key Y belongs to a universe which depends on the encryption key X. The observation of a plurality of transmissions reveals a plurality of functions F, and the values ​​of keys X and Y are located at the intersection of these functions. It is preferable to avoid this situation. It is therefore recommended either to use, for key X or key Y, values ​​that change during transmissions, or to use encryption functions such that, for each observation of exchanges of the triplet "message, encrypted number, encrypted hash", the universe of keys Y for each possible X is large; thus making the universe resulting from the intersection of these universes deducible at each observation large. It is not recommended to take, for key Y, the randomly generated mixing number x.More precisely, if we use the mixing number x as the encryption key Y, or if we calculate the key Y as a function of the mixing number x using a defined formula, knowing the encrypted value C of the mixing number x encrypted with the key X, the mixing number x, and therefore Y, becomes another function G of the key X; and the keys X and Y would then be at the intersection of the function F and this new function G. Preferably, we renew the key X or the key Y after each exchange.

[0337] The device may further include a counter of consecutive failed verification attempts, which triggers its blocking when a defined number is reached, the device being able to be unlocked during the renewal of the encryption key used to encrypt the mixing number or the encryption key used to encrypt the hash.

[0338] Alternatively, the apparatus may impose a predetermined number of successive unsuccessful verification attempts on messages arriving or sent by the same sender, after which predetermined number, and after a fixed period, the apparatus places the messages received or the message sent by the same sender in a queue or, preferably, ignores them, before attempting again either to decrypt the messages placed in the queue, or to resume the decryption of messages which continue to arrive after the expiry of the fixed period. This approach is advantageously implemented by a device returning to the sender of the messages placed in a queue or ignored, a response message to inform him of the processing of his message.For example, three messages received consecutively from a sender that cannot be verified may cause the device to reject messages sent by that same sender for one minute, after informing the sender that their messages were being ignored during that time.

[0339] Second method of verifying the integrity of a message

[0340] A second variant of the method according to the invention is a method making it possible to verify by means of the apparatus the integrity of a message coming from a sender, the method comprising the steps consisting of: i. receive, by means of the device, the message, the third encrypted data set and the encrypted mixer number, ii. decrypt the mixer number and the third data set, and iii. implement steps a) to c), the integrity of the message being ensured if the hash obtained in step b) and the third dataset decrypted in step ii) are identical.

[0341] Decryption can be performed using an encryption key kept secret between the device and the sender.

[0342] Preferably, the mixing number is kept secret and a renewable key having the size of the hash (third data set) is used, in particular with an XOR as an encryption function.

[0343] Alternatively, the mixer number is kept secret and a non-renewed symmetric key with a symmetric encryption function is used.

[0344] Alternatively, the mixer number is kept secret and a non-renewed asymmetric key pair with an asymmetric encryption function is used.

[0345] Alternatively, the mixer number is kept secret and a non-renewed symmetric key with a symmetric encryption function is used.

[0346] Alternatively, the mixing number is a renewable key and another renewable key having the size of the hash (third data set) is used, notably with an XOR as an encryption function.

[0347] Alternatively, the mixing number is a renewable key and a non-renewable key having the size of the hash (third data set) is used, notably with an XOR as an encryption function.

[0348] Alternatively, the mixing number is a renewable key and a non-renewed symmetric key with a symmetric encryption function is used.

[0349] Alternatively, the mixing number is a renewable key and a non-renewed asymmetric key is used with an asymmetric encryption function.

[0350] Preferably, the mixer number identifier is exchanged between the sender and the device, each of which can retrieve the corresponding mixer number from a stored list of mixer numbers.

[0351] In another exemplary embodiment, the mixer number is randomly generated after each use. This mixer number can be encrypted by a single-use key. Alternatively, the mixer number is encrypted by a symmetric or asymmetric function. Preferably, the method according to this second variant of the invention comprises, before step i, the steps consisting of: - generating, by the sender, the mixer number, - mixing the mixer number with the message, using the mixing function, - hash the data resulting from the previous step using the hash function, - encrypt the hash resulting from the previous step and the formation of the third data set, - encrypt the mixer number, and - send the message, the third encrypted data set and the encrypted mixer number to the device.

[0352] These steps are performed by the authentic sender and allow the detection of alteration of the message by an unauthorized third party.

[0353] The decryption in step ii of the mixing number and the third data set is preferably carried out by the apparatus.

[0354] Preferably, the encryption of the mixing number is performed using a one-time key, and the encryption of the third data set is performed using a symmetric key, the symmetric key preferably being renewed occasionally.

[0355] Alternatively, the encryption of the mixing number is performed using a symmetric key, and the encryption of the third data set is performed using a one-time key, the symmetric key preferably being renewed occasionally.

[0356] The encryption of the mixing number and the encryption of the third data set may also be of the same type, or of different types, these types of encryption being able to use symmetric keys or asymmetric keys.

[0357] If an asymmetric key pair is used for the encryption of the mixing number, the private key of this pair is preferably kept by the device, the corresponding public key then being known to the sender.

[0358] The encryption of the third data set can be carried out using a private key kept by the sender, the corresponding public key then being known to the device.

[0359] Thus, by decrypting the mixer number and the third data set, the device is able to certify the identity of the sender.

[0360] The encryption of the mixer number and that of the third data set can be carried out using the same encryption function, in particular when the encryption of the mixer number is asymmetric.

[0361] Alternatively, the encryption of the mixing number and that of the third data set are performed by two different encryption functions.

[0362] Preferably, the types of encryption functions to be used are part of the configuration of the sender and the device, before establishing communication between the latter two.

[0363] Third method of verifying the integrity of a message

[0364] A third variant of the method according to the invention is a method in which the first data set is present in the device and the second data set is present in a second device, the method comprising the steps of: i. implement steps a) and b), ii. encrypt the mixing number, iii. send, by means of the device to the second device, the encrypted mixer number, iv. receive, by means of the device, an encrypted hash of the second data set, v. decrypt the encrypted hash, and vi. implement step c).

[0365] Decryption may be performed using an encryption key kept secret between the device and the sender.

[0366] Preferably, the mixing number is kept secret and a renewable key having the size of the hash is used, in particular with an XOR as an encryption function.

[0367] Alternatively, the mixer number is kept secret and a non-renewed symmetric key with a symmetric encryption function is used.

[0368] Alternatively, the mixer number is kept secret and a non-renewed asymmetric key pair with an asymmetric encryption function is used.

[0369] Alternatively, the mixer number is kept secret and a non-renewed symmetric key with a symmetric encryption function is used.

[0370] Alternatively, the mixing number is a renewable key and another renewable key having the size of the hash is used, in particular with an XOR as an encryption function.

[0371] Alternatively, the mixing number is a renewable key and a non-renewable key having the size of the hash is used, in particular with an XOR as an encryption function.

[0372] Alternatively, the mixing number is a renewable key and a non-renewed symmetric key with a symmetric encryption function is used.

[0373] Alternatively, the mixing number is a renewable key and a non-renewed asymmetric key is used with an asymmetric encryption function.

[0374] Preferably, the mixer number identifier is exchanged between the sender and the device, each of which can retrieve the corresponding mixer number from a stored list of mixer numbers.

[0375] In another exemplary embodiment, the mixer number is randomly generated after each use. This mixer number may be encrypted by a one-time key. The mixer number may also be encrypted by a symmetric or asymmetric function.

[0376] Preferably, the method according to this third variant of the invention comprises, between steps iii and iv, the steps consisting of: - receive, by means of the second device, the encrypted mixer number, - decipher the mixing number, - create a modified copy of the second dataset using the mixer number and the blend function, - hash the modified copy of the second dataset using the hash function, - encrypt the resulting hash from the previous step and form the third dataset, and - send, by means of the second device to the device, the encrypted hash of the second data set.

[0377] The encryption of the mixing number in step ii and the decryption of the encrypted hash in step v are preferably performed by the apparatus.

[0378] Preferably, the encryption of the mixing number is performed using a symmetric encryption key shared with the second device.

[0379] The encryption of the hash can be done using a one-time key and the encryption of the mixing number can be done using a symmetric key that is renewed occasionally.

[0380] Alternatively, the encryption of the mixing number is performed using a one-time key and the encryption of the hash is performed using a symmetric key that is renewed occasionally.

[0381] Mixing number encryption and hash encryption may also be of the same type, or of different types, where these types of encryption may use symmetric keys, including one-time keys, or asymmetric keys.

[0382] Method for generating shared quantum keys

[0383] The invention can be used in quantum communication methods, in particular in Quantum Key Distribution E91, where a pair of entangled photons is used to generate a secret shared between two photon receivers.

[0384] Another aspect of the invention relates to a method for generating a shared quantum key using a quantum communication system, the system comprising: • an emitter of entangled photons, configured to generate at least one pair of entangled photons comprising a first photon emitted on a first propagation path, and simultaneously a second photon emitted on a second propagation path different from the first propagation path; • a first receiver arranged on the first propagation path, comprising a first polarization measurement base configured to measure a polarization state of a photon received by the first receiver; and • a second receiver arranged on the second propagation path, comprising a second polarization measurement base configured to measuring a polarization state of a photon received by the second receiver, the clocks of the two receivers being synchronized such that two photons of the same pair of photons arriving at the receivers arrive at the same time according to the clocks of the receivers reached;

[0385] in which the first receiver establishes a first list comprising the reception dates and a second list comprising these reception dates and the polarization states of the photons received by the first receiver, and the second receiver establishes a third list comprising the reception dates and a fourth list comprising these reception dates and the complementary polarization states of the photons received by the second receiver;

[0386] wherein the first list and / or the third list are exchanged between the first receiver and the second receiver and are preferably electronically signed;

[0387] wherein, upon receiving the third and / or first list, respectively, the first receiver and / or the second receiver establishes a fifth list comprising the dates on which the two photons of the same pairs were received by the two receivers, given that some photons may have been lost during transmission between the transmitter and one or both of the two receivers;

[0388] wherein, if only one of the two receivers establishes the fifth list, said fifth list is transmitted, preferably electronically signed, to the other receiver, such that the first receiver and the second receiver respectively establish a sixth list and a seventh list of polarization states of the photons as received by the first receiver, the sixth list being derived from the second list and the fifth list, the seventh list being derived from the fourth list and the fifth list, each polarization state on the sixth list of a photon received at a time marked on the fifth list being the same polarization state as that of the corresponding photon received at the same time and marked on the second list, each polarization state on the seventh list of a photon received at a time marked on the fifth list being the complementary polarization state of the corresponding photon received at the same time and marked on the fourth list;;

[0389] wherein the respective signatures of the sixth list and the seventh list are exchanged between the first and second receivers, according to the method of the invention, preferably with a mixing number renewed each time and a renewed single-use key used for the encryption of the hash;

[0390] wherein said sixth and seventh lists can be used as a shared list of random bits. From this shared list, one-time keys or lists of random rotation angles of the polarization measurement bases can, for example, be extracted.

[0391] A signed message may be exchanged between the two receivers before using the sixth and seventh lists as one-time keys.

[0392] The polarization measuring bases can be made to rotate randomly and simultaneously by the same angle kept secret between the two receivers.

[0393] The sixth and seventh lists can be used as lists of random rotation angles of the polarization measurement bases.

[0394] The photons are preferably sent in a fixed polarization which is not the polarization of the photons which can be measured by the receivers, the photons being able for example to be sent in circular polarization, while being detected in orthogonal linear polarization states, or sent in linear polarization in a direction which is not the direction of the polarization in which they can be detected, preferably fixed at 45° from the direction of linear polarization in which the polarizations of the photons are detected by the receivers.

[0395] The direction of the polarization angle at which the polarizations are detected by the receivers may be changed periodically and randomly by the same angle on both receivers, the change preferably being a 0° or 45° change and, preferably, the linear polarization angle at the transmitter being changed by the same angle if the transmitter actually emits the linearly polarized photons. The change may for example occur every millisecond. This prevents a spy device from sending pairs of photons to both receivers in known polarizations that can be detected by the receivers, one of the photons being in the complementary polarization of the other and arriving at the receivers at the same time according to the "synchronized" clocks, because the direction in which the photons can be detected by the receivers may not be known by the spy device.

[0396] The polarization angle can be modified, for example, by means of a bypass circuit for the photons upstream of the receivers, a first switch being able to deflect the incident photon towards a photon polarization rotation device and a second switch making it possible to send the photon leaving said polarization rotation device towards said receiver, such that, in a first mode, the photons bypass the polarization rotation device, while in another mode, the photons pass through the polarization rotation device before entering the receivers. The photon rotation device can be made, for example, of a chiral material such as CdSe nanoparticles of 1.4 to 2.4 qm (source: inorganic Nanostructures with Strong Chiroptical Activity Anastasia Visheratina & Nicholas A.Kotov* University of Michigan), or such as a device consisting of a first birefringent prism splitting the light into two beams of linearly polarized light which each pass through two quarter-wave plates forming an angle between them, such that the light leaves the second quarter-wave plate. linearly polarized at an angle to the direction of polarization at which it reaches the first quarter-wave plate, the two beams of linearly polarized light leaving the second quarter-wave plates being united into a single beam by passing through a second birefringent prism.

[0397] The angle changes may be fixed in accordance with one-time keys shared between the two receivers and, if necessary, the sender. If the angle change is applied only to the two receivers, for example, if the sender sends the photons in a circularly polarized state while the readers read the photons in a linearly polarized state, the one-time key may be renewed using keys generated by the shared Quantum Key generation process described herein.

[0398] By "complementary polarization state of a given photon" is meant the polarization state in which the photon entangled with said given photon should be found.

[0399] Furthermore, the photon path is preferably physically protected against the insertion of a spy device in a first zone, in its part where the photons propagate without being entangled. For example, if the photon path is longer by a length measured between the photon emitter and the second photon receiver than between the emitter and the first photon receiver, the path followed by the photon between the emitter and the second receiver is physically controlled at least in the vicinity of the second receiver for said measured length.

[0400] For example, the said length can be physically measured, in particular if the photons propagate in optical fibers. Similarly, and in particular during propagation in free space, the measurement can be carried out, for example, by placing clocks that are actually synchronized on the two receivers (as opposed to the synchronized clocks described above), and by having verified at the time of this measurement that no spy device has been inserted between the transmitter and the receivers.

[0401] Here again, the path of the photon is preferably physically protected in a second zone located upstream of the first zone, if it exists, or upstream of the detector, if the first zone does not exist, against the insertion of a spy device. This second zone is configured so that the photon propagates there for a time greater than the uncertainty of the arrival time at which the photons are detected at the two receivers.

[0402] If a spy photon detector and emitter is introduced upstream of the first detector, this spy detector will detect the photons and their polarization before re-emitting photons of the same polarization towards the second detector. However, this re-emitted photon will have to pass through the first zone and the second zone, thus arriving at a different time than when it would have arrived if no spy device had interfered, and this time difference being perceptible by the second receiver.

[0403] A spy transmitter can send to the first legitimate receiver a first photon entangled with a second photon and detect the polarization state of the first entangled photon by checking the polarization of the second photon. However, to transmit this polarization state to the second transmitter, it will have to send a photon polarized in the appropriate state, but this photon will first have to propagate towards the second protected area, then travel through the protected area, this requiring more time and, consequently, will arrive at a different time than that at which the initial spy photon was detected by the first receiver.

[0404] On the other hand, if a spy device sends to the second receiver a first photon entangled with a second photon and detects its polarization state, it could then send to the first receiver a photon having the same polarization; however, this photon will arrive after the second receiver has received its detected photon, therefore at a time, according to the "synchronized" clocks, different from the time when the other photon arrived at the second receiver.

[0405] The sizes of the first and third lists are preferably chosen with a tolerance coefficient such that the sixth and seventh lists have a reasonable chance, for example at least a 50% chance of being equal, if nothing has interfered during the process of transmitting the entangled photons. For example, if the entangled photons are read in corresponding states on the two receivers in 99.9% of cases, i.e. if the reading of their polarization state is correct in 99.9% of cases, the sixth and seventh lists may have a length of 500 bits and the first and second lists may comprise 5000 successive reception times if 90% of the entangled photons are lost between the photon transmitter and the receivers, each photon receiver, regardless of the receiver, having only a 10% chance that its entangled photon has been received by the other receiver.

[0406] Fourth method of verifying the integrity of a message

[0407] A fourth variant of the method according to the invention is a method making it possible to verify that a data set present in the device has not been modified between two times d1 and d2, this data set constituting, at time d1, the first data set and, at time d2, the second data set, the method comprising the steps consisting of: i. implement steps a) and b), ii. securely record, using the device, the mixer number and the hash obtained in step b), iii. create a modified copy of the second dataset using the mixer number and the mix function, iv. hash the modified copy using the hash function to form the third dataset, and v. implement step c).

[0408] Advantageously, the method according to this fourth variant does not require the data set to be stored securely. Computer program product

[0409] The invention also relates to a computer program product containing instructions readable by a processor of an apparatus for implementing the method according to the invention, according to any one of the variants defined above. Brief description of the drawings

[0410] The invention may be better understood by reading the detailed description which follows, non-limiting examples of its implementation, and by examining the appended drawings, in which:

[0411] [Fig. 1 A] partially and schematically represents a quantum communication system according to the invention,

[0412] [Fig.lB] partially and schematically represents another quantum communication system according to the invention,

[0413] [Fig.2A] partially and schematically represents a linearly polarized photon,

[0414] [Fig.2B] partially and schematically represents a circularly polarized photon,

[0415] [Fig.3] [Fig.3] schematically represents details of transmission of photons from the transmitter to the receivers,

[0416] [Fig.4A] partially and schematically represents an example of an optical selector according to the invention,

[0417] [Fig.4B] partially and schematically represents a variant of the selector of [Fig.4A],

[0418] [Fig.4C] partially and schematically represents another example of an optical selector according to the invention,

[0419] [Fig.5A][Fig.5B] [Fig.5A] and [Fig.5B] schematically represent an example of a polarization direction modifier comprising quarter-wave plates,

[0420] [Fig.5C] [Fig.5C] schematically represents another example of a polarization direction modifier comprising a chiral material,

[0421] [Fig.6] [Fig.6] schematically represents an example of a polarization phase modifier,

[0422] [Fig.7] partially and schematically represents an example of an instrument for absorbing a linearly polarized photon,

[0423] [Fig.8] partially and schematically represents another example of an instrument absorption of a linearly polarized photon,

[0424] [Fig.9] partially and schematically represents an example of a receiver of the second photon comprising a doped fiber amplifier,

[0425] [Fig. 10A] partially and schematically represents an example of a measuring instrument of the second receiver comprising a succession of semi-reflecting blades,

[0426] [Fig. 10B] partially and schematically represents an example of a Young interferometer used for the measuring instrument of the second receiver,

[0427] [Fig. 11A] is a functional diagram partially illustrating an example of operation of a quantum communication system for transmitting a bit 0,

[0428] [Fig. 11B] is a functional diagram partially illustrating an example of operation of a quantum communication system for transmitting a bit 1,

[0429] [Fig. 12] is a functional diagram partially illustrating an example of operation of a quantum communication system for transmitting a series of discrete values,

[0430] [Fig. 13] is a functional diagram partially illustrating an example of a method for timestamping the arrival of a photon in a receiver,

[0431] [Fig. 14] illustrates in a partial and schematic manner the possibility of placing an "anti-noise" device in front of the amplifier,

[0432] [Fig. 15] shows in a partial and schematic manner the possibility of using the system according to the invention to establish two-way communication between two locations,

[0433] [Fig. 16] [Fig. 16] illustrates an alternative implementation of a quantum communication system according to the invention,

[0434] [Fig. 17] [Fig. 17] schematically illustrates a physical protection of the quantum communication system according to the invention,

[0435] [Fig. 18] [Fig. 18] schematically illustrates an optical protection of the entangled photons of the quantum communication system according to the invention,

[0436] [Fig. 19] [Fig. 19] schematically illustrates an example of a method for calculating a hash of a data set. Detailed description

[0437] [Fig.lA] illustrates a quantum communication system 1 according to the invention. The system comprises an emitter 2 emitting a pair of entangled photons (PI, P2), the first photon PI propagating on a propagation path DI and the second photon D2 propagating on a propagation path D2 different from the path D1. The photons PI and P2 are emitted simultaneously.

[0438] Due to the nature of light and the wave-particle duality of the photon, the terms "wave", "photon" and "particle" are used interchangeably in the following to designate the product emitted by emitter 2.

[0439] The terms "measuring instrument" and "absorption instrument" are used interchangeably to designate an instrument absorbing a photon according to a certain polarization.

[0440] The system 1 comprises a first receiver 3, located on the propagation path DI of the first photon PI, and a second receiver 4, located on the propagation path D2 of the second photon P2.

[0441] Receiver 3 is closer to emitter 2 than receiver 4, so that photon PI reaches it before photon P2 reaches receiver 4. Photon P2 reaches receiver 4, for example, after an additional travel time ttta corresponding to an additional travel path Ltra.

[0442] In the example considered, the receiver 3 comprises a complex absorber 31 comprising a polarization modifier 32 and an absorption instrument 35.

[0443] The complex absorber 31 is configured to absorb the photon in a polarization state selected from several pairs of different complementary polarizations, preferably at least three pairs.

[0444] The polarization modifier 31 is configured to transmit the PI photon according to the selected pair of complementary polarizations and the absorption instrument 35 makes it possible to determine in which of the two states of the pair is the PL photon. Before entering the absorption instrument 35, the polarization state of the PI photon is a superposition of the two states of the selected pair, weighted by certain probabilities, for example in an equiprobable manner.

[0445] [Fig. 1B] illustrates another example of a quantum communication system 1 according to the invention. In this example, the receiver 3 comprises two measuring instruments 35 arranged to measure the quantum state of the first photon PI, and an optical selector 30 arranged upstream of the measuring instruments 35 and configured to send the first photon PI either to a birefringent prism 36 which conducts the photon, according to the linear direction of its polarization, on paths D1' or D1" then to one or other of the measuring instruments 35, or prevents it from being measured, for example by reflecting it on a propagation path D3 different from the path DL

[0446] The direction D3 is notably chosen so that the photon PI is not absorbed before its entangled photon is multiplied at the second receiver 4.

[0447] The system 1 preferably comprises, as illustrated, a device 5 for protecting the quantum state of a photon arranged close to the receiver 3, in particular on the propagation path D3 in the example considered.

[0448] This device makes it possible, for example, to "trap" the photon PI in the case where it is reflected by the optical selector 30 on the path D3, in order, for example, to prevent it from is measured or absorbed at least until the second photon P2 has reached the second receiver 4. A 5D photon detector (not shown) may be placed at the end of the device 5 to detect the photons captured there, after their entangled photons have reached the second receiver.

[0449] The second receiver 4 comprises an optical amplifier 40 making it possible to multiply the second photon P2 while preserving its polarization and a measuring instrument 45 making it possible to measure the average polarization of the multiplied photons.

[0450] The transmission of PI and P2 photons can be done in various ways, and in various media. The photons propagate, for example, in an optical fiber or a waveguide, or freely in space, the space being empty or filled with gas.

[0451] Photons can pass through several media, having different refractive indices. For example, anti-reflection plates can be inserted between two media crossed, if necessary, in order to avoid unwanted optical phenomena, in particular a Fresnel reflection of the waves emitted by the transmitter 2.

[0452] The emitter 2 comprises, for example, one or more selected lenses of sufficient size so that the photons reach their respective receiver with low diffraction, for example allowing at least 99.99% of the emitted light to reach the receiver.

[0453] The emitter 2 may further comprise a system, in particular an electronic device, making it possible to adjust the initial directions in which the photons PI and P2 are respectively emitted.

[0454] This adjustment can, for example, take into account the different refractive indices of the media crossed, and the modification of the trajectory of the photons which can result, for example for a photon emitted from space which enters the atmosphere.

[0455] The wavelength of the emitted wave is for example selected according to the medium(s) to be crossed; for example, photons in the infrared range will preferably be used when they have to pass through the atmosphere or air.

[0456] The transmitter 2 generates, for example, pairs of entangled photons using the spontaneous parametric downconversion (SPDC) method. The transmitter 2 is, for example, configured to emit on average less than one pair per unit of time, for example one pair per nanosecond, which corresponds to a photon transmission frequency of 1 GHz.

[0457] When they are emitted, the photons P are for example linearly polarized, that is to say that the corresponding electromagnetic wave has an electric field whose direction is perpendicular to its direction of propagation D. Where appropriate, the polarization of the photons can be vertical V or horizontal H, as illustrated in [Fig.2A].

[0458] The quantum state corresponding to the polarization of photons is sometimes undetermined until it has been measured or absorbed. Before being measured, the quantum state of the photon is therefore sometimes considered as the superposition of possible states, namely, in the example considered, as the superposition of a polarization at an angle of 45° and a polarization at an angle of -45°.

[0459] In the variant illustrated in [Fig.2B], the P photons, when emitted, are circularly polarized, that is to say that the direction of the corresponding electric field changes according to a rotational movement, while its norm remains constant.

[0460] Where appropriate, the polarization of the photons is defined by the direction of rotation of the electric field, either clockwise Cl or counterclockwise C2. Before being measured, the linearly polarized photons are in an indeterminate quantum state, considered as the superposition of two circular polarization states of opposite rotation directions.

[0461] In certain cases, two quarter-wave plates 6 and 8 can be introduced into the photon propagation paths, between the transmitter 2 and the receivers 3 and / or 4, as illustrated in [Fig.3].

[0462] The blade 6, depending on its orientation, converts for example the linear polarization of a photon into circular polarization by advancing or delaying the electromagnetic waves propagating along an axis perpendicular to the ordinary axis of the crystal with an electric field perpendicular to this same axis relative to the wave having an electric field parallel to said ordinary axis.

[0463] The photons emerging from the plate 6 are for example transmitted by an optical fiber 7 to another quarter-wave plate which converts the circularly polarized fields into linearly polarized fields, before propagating towards the receivers 3 or 4.

[0464] This conversion of the polarization of the emitted photons makes it possible in particular to not have to take into consideration at the receiver level the direction of the polarization of the photons emitted by the transmitter.

[0465] The optical selector 30 can be implemented in various ways, some examples of which are illustrated in Figures 4A to 4D.

[0466] The optical selector 30 comprises, for example, a liquid crystal controlled mirror as illustrated in [Fig.4A], comprising a plate 370 enclosing liquid crystals. For example, electrodes 315 and 320 are placed on opposite sides of the plate 370 in order to subject the liquid crystals to an electric field, making it possible to control their refractive index nc.

[0467] Depending on the refractive index nc, the incident photon PI can be reflected on a propagation path D3, or it can pass through the plate 370 and be transmitted on a propagation path Dl', which can be identical or different from the path Dl, towards the measuring instrument 35.

[0468] In a variant illustrated in [Fig.4B], the photon PI passes through the liquid crystal plate 370 and comes out along D3 or DI', the directions D1, DI' and D3 being, in the example considered, parallel.

[0469] A mirror 325, in particular a Bragg mirror, can be placed on the propagation axis D3 in order to reflect the photon in another direction, for example towards the protection device 5.

[0470] Anti-reflection blades can advantageously be placed on each of the faces of the blade 370 and adjusted according to the entry and exit angles of the photon when it passes through it.

[0471] In the variant illustrated in [Fig.4C], the optical selector 30 is a mirror controlled by non-linear fibers. It comprises two optical fibers 330 and 335. The fiber 335 is for example formed from a non-linear material.

[0472] The first photon PI, upon arrival at the first receiver, enters the fiber 330. It is possible to choose to simultaneously illuminate the fiber 335 with a light signal F, also called a "control signal".

[0473] The signal F is a high intensity light wave, for example emitted by a laser, and of a wavelength different from that of the photon PL

[0474] If the fiber 335 is illuminated by the signal F, the photon PI remains in the fiber 330 before, for example, passing through a prism 345 at the fiber outlet arranged on a propagation path D3. Similar to what was described above, a mirror 325, in particular a Bragg mirror, can be placed on the propagation axis D3 in order to reflect the photon in a desired direction, for example towards the protection device 5 or, directly back into the fiber 330.

[0475] If the fiber 335 is not illuminated by the signal F, the photon PI is transmitted from the fiber 330 to the fiber 335. The photon PI emerges from the fiber 335 and passes through, for example, a prism 340 before being transmitted, for example, to the measuring instrument 35. The prism 340 is preferably made of a dispersive material making it possible to cause the illumination light to emerge from a different location and in a different direction from that of the photon. A Bragg mirror (not shown) returning only said illumination light and allowing the photon to pass may be placed between the fiber 335 and the prism 340, for example to reflect said illumination light in a direction other than toward the prism 340 or even into the fiber.

[0476] Anti-reflection plates (not shown) can be placed at the input and output of the prisms 340 and 345 and adjusted to the wavelength of the PL photon.

[0477] We will now describe various ways of implementing the polarization modifier 32 of the system of [Fig.lB].

[0478] The polarization modifier 32 preferably comprises a polarization direction modifier 32a disposed upstream of a phase modifier 32b.

[0479] In a first exemplary embodiment of modification of the polarization direction, the polarization direction modifier 32a comprises a stack of plates 560, in particular quarter-wave plates, oriented differently from one another, as illustrated in [Fig.5A], such that a circular wave 558 entering one of these quarter-wave plates emerges as a wave 511 linearly polarized in a direction associated with said plate.

[0480] These blades can be designed to operate with waves 558 penetrating them in a direction parallel to the bisector of their edges 521 and 522. These blades are preferably composed of uniaxial birefringent crystals such as, for example, rutile. This birefringent crystal can compose their entire mass or be concentrated on a slice, for example on one of the edges 523 crossed by the wave 558, as illustrated in [Fig.5A].

[0481] These blades can be juxtaposed with each other to form a structure 524, as illustrated in [Fig.5B], so that the outgoing waves 511 or 512 have a linear polarization whose direction of the electric field depends on the place of penetration, in the assembly 524, of two circularly polarized waves 558 or 559 with a direction parallel to the bisector of the edges 521 and 522.

[0482] Thus, a wave 556 of determined direction and linear polarization penetrating into the quarter-wave plate 551 passes through it in the direction 557 to become circularly polarized there before penetrating into a crystal 552 whose refractive index is adjustable, for example under the effect of an electric field generated by electrodes 516, then preferably penetrates into another crystal 553 whose refractive index is also adjustable, for example under the effect of an electric field generated by electrodes 517 generating an electric field perpendicular to the field generated by the electrodes 516.

[0483] Two circularly polarized waves 558 and 559 then emerge from the crystal 553 and enter the assembly 524 at different locations depending on the selection of the refractive index imposed on the crystal 553. The direction of the light ray being different depending on these locations, the direction of the edges 520 and 521 is preferably different for each element 560 of the assembly 524.

[0484] In the diagram illustrated in [Fig.5B], waves 511 and 512 therefore constitute two possibilities for the light ray to pass through assembly 524. These waves leave assembly 524 linearly polarized in different directions and having the same direction of propagation but in different places on the edge 514 of assembly 524. They penetrate another crystal 554 whose refractive index is electrically adjustable by electrodes 518 then, preferably, yet another crystal 555 whose refractive index is also adjustable by electrodes 519 creating an electric field perpendicular to the field created by electrodes 518, and whose voltages are adjusted according to the refractive index selected for crystals 552 and 553, so that the light waves always emerge from crystal 555 as a wave 513 of the same direction at the same location 515.

[0485] The crystals 552, 553, 554 and 555 are, for example, E7 liquid crystals from Merck, to the terminals of which the electrodes apply, for example, voltages between 0 and 5000V if the distance between the electrodes of each of the pairs is 5 mm, making it possible to vary their refractive indices between 1.5 and 1.67. The electrodes are preferably covered with a dielectric film. These refractive indices modified by the electric fields can be different depending on the relative direction of the electric field of the light and depending on the direction of the electric field, the application of successive perpendicular electric voltages makes it possible to modify the refractive index for each of the two components of said light, this being the superposition of the waves whose electric field is perpendicular to [Fig.5B] and the waves whose electric field is perpendicular to the direction of propagation and in the plane of the figure.

[0486] In a second exemplary embodiment (not shown) of modification of the polarization direction, the linearly polarized wave in a determined direction enters a first quarter-wave plate transforming its polarization into circular polarization, then a second quarter-wave plate transforming this circular polarization into a linear polarization in an adjustable direction depending on the orientation of this second quarter-wave plate. The orientation of the second quarter-wave plate is obtained for example by mechanical control of a sensor, or an electrically controlled device allowing its rotation, for example by rubbing on a shaft set in motion by a piezoelectric material or by an electric motor device, for example direct current.

[0487] In a third example illustrated in [Fig.5C], liquid crystals are used to control the rotation of the linear electric field of the incident photons 526 linearly polarized in the same direction of polarization, which begin for example by crossing, preferably perpendicularly, one of two transparent electrodes 527 of 0.2 pm coated on one of its faces 528 with a material orienting the liquid crystal particles 529 adjacent to said face 527 in the direction of the polarization of the incident photons 526, then cross the liquid crystal 529 over 2 pm before crossing the second transparent electrode 527 whose face 528, preferably parallel to the first electrode, is also coated with a material making it possible to align the liquid crystals but in a direction perpendicular to the direction imposed by the coating of the first electrode.The direction of the liquid crystals between the two electrodes is thus gradually modified from 0° to, for example, 60° relative to their initial orientation. The application of an electrical voltage comprised by . example between 0 and 1 V gradually reorients the liquid crystals to impose a direction on them in the axis of the direction of propagation of the photons, thus gradually reducing the difference in refractive index of the liquid crystals between the two polarizations perpendicular to the displacement of the photons and the rotating power of the device. This device therefore makes it possible to continuously select the output direction of the polarization of the incident photon between 0 and 60°.

[0488] Devices such as that illustrated in [Fig.5B] are advantageously used in a device similar to that described above and illustrated in [Fig.5A], for example placed between the blades 524 and 554, each of for example 4 elements 560 making it possible to place the linear polarization of an incident photon in one of four precise directions, for example -90°, -45°, 0° and +45°, then each of the devices described in [Fig.5B] placed in succession, and preferably aligned with the direction of propagation of the photons leaving the devices 560 which precede them, making it possible to add to this rotation a rotation of any angle for example between 0 and 45°.

[0489] [Fig. 6] illustrates a polarization phase modifier 32b according to the invention. The phase modifier 32b comprises a first birefringent plate or prism 370 arranged to divide the incident photon PI of polarization field E into two electromagnetic waves of linear polarization Ei and E2 on two different axes Xi and x2.

[0490] A delay plate 321 of variable refractive index is placed on the second axis x2, for example comprising a Pockels cell such as lithium niobate, controlled by electrodes 322 or a non-linear material, so as to cause the wave E2 oriented along the second axis x2 to acquire a predetermined phase shift relative to the wave Ei oriented along the first axis xL.

[0491] Another birefringent plate 370, for example made of paratellurite, is arranged at the output of the phase modifier 32b, making it possible to combine along the same axis x the two waves whose polarization fields E1 and E2 are perpendicular into a wave or photon PI of field E' having acquired a phase shift with respect to the field E. Alternatively, to take advantage of the different modification of the refractive index of the crystal according to the direction of the electric field of the light compared to the direction of the electric field modifying the refractive index, a simple Pockels cell 321 can be used with the electrodes 322 but without the plates 370.

[0492] The measuring instruments 35 of the first receiver 3 may be of various types and comprise various elements. These elements depend in particular on the nature of the polarization of the photon PI when it is emitted by the transmitter 2. Certain examples are illustrated in FIGS. 7 and 8 and described below.

[0493] In the example illustrated in [Fig.7], the measuring instrument 35 comprises a polarizing filter 350 arranged on the propagation path DI of the photon PI and a detector of photons 355 arranged on the same propagation path, downstream of filter 350.

[0494] The polarizing filter 350 only allows photons with a certain linear polarization to pass through and absorbs those with a polarization perpendicular to them. It therefore makes it possible to select photons with a linear polarization of a certain direction.

[0495] In the example considered, the polarizing filter 350 is a grid formed of wires, for example metallic, vertical. It only allows photons with horizontal linear polarization H to pass.

[0496] In a variant illustrated in [Fig.8], the measuring instrument 35 comprises an anisotropic plate 360, for example a birefringent blade, a birefringent prism or two birefringent prisms joined together. The plate is for example made of barium beta borate (BaB2O4, BBO).

[0497] The photon PI whose quantum state is to be measured reaches the plate 360 ​​on an incident propagation path D1, and is transmitted on one of two propagation paths DI 1 or D12, depending for example on whether its polarization is in the plane of plate 360 ​​(that is to say, perpendicular to the plane of [Fig.8]), or normal to the plane of plate 360.

[0498] The measuring instrument 35 further comprises two detectors 355, each placed on a propagation path DU or D12 of the photon PL

[0499] In this example and unlike the polarizing filter, all photons can be detected by the detectors 355, regardless of their polarization.

[0500] In some embodiments, a quarter-wave plate is placed upstream of the anisotropic plate 360 ​​in order to convert a circular polarization of a photon into linear polarization, and thus detect the direction of rotation of a circularly polarized photon.

[0501] The second receiver 4 may comprise different types of optical amplifier 40 and measuring instrument 45.

[0502] For example, a doped fiber amplifier is used as illustrated in [Fig.9].

[0503] In this example, the amplifier 40 comprises a fiber 400, in particular a fiber made of non-linear material, into which the second photon P2 is introduced after having passed through a dichroic prism 451 when it reaches the receiver 4.

[0504] An electromagnetic control wave F serving to supply energy and multiply the photon P2 is introduced by a fiber 450 into the same dichroic prism 451 at a point and with a direction such that it emerges from the fiber 400 just like the photon P2, the photon P2 and the control wave F having different wavelengths.

[0505] The control wave F is preferably of high light intensity and preferably of shorter wavelength than that of the photon P2.

[0506] During its passage through the fiber 400 and under the effect of the luminous flux F, the photon P2 is multiplied into N photons P20, then these N photons and the flux F pass through a second dichroic prism 452 from which they emerge in different directions. The N photons are then advantageously directed towards a measuring instrument 45, making it possible to determine the polarization of the luminous flux and examples of embodiment of which are given in [Fig. 10A] and 10B.

[0507] The information transmitted by the first receiver can be deduced from the measurements of the measuring instrument 45, because the amplification of the photon P2 by the device 40 preserves its polarization.

[0508] In particular, if the photon P2 is the entangled photon of a photon PI absorbed in one of two complementary polarizations known to the first receiver, the N demultiplied photons P20 are measured with a polarization which can be deduced from the absorption polarization of the photon PI using the Jones matrix calculated during a calibration as described above.

[0509] The measuring instrument 45 may comprise a succession of semi-reflecting plates 452 and a mirror 453, as illustrated in [Fig. 10A]. The plates 452 and the mirror 453 direct the multiplied photons P20, which form a luminous flux, for example towards prisms made of birefringent materials 350 preferably having an equal intensity. The filters 350 divide the luminous flux into two orthogonally polarized luminous fluxes, so that the detectors 455 can either determine the intensity of said flux in each of the orthogonal directions, or determine the phase shift between the two orthogonal components of the flux, for example by means of a Michelson interferometer or a Young slit interferometer.

[0510] The interferometers are preferably arranged so that the light paths of the two orthogonal components are identical, the light flux from the multiplication of a single photon being very brief. The use of a plurality of pairs of orthogonal directions, for example offset by 45° from each other, advantageously makes it possible to measure the polarization several times, that is to say the direction of the polarization as well as the phase shift between the two directions, thus allowing greater precision of the measurement.

[0511] [Fig. 10B] represents an example of such a Young's slit interferometer. Two waves 460 and 463 come from the prism 350. The wave 460 passes for example through a prism 461 straightening its direction of propagation so that it becomes at 462 parallel to the wave 463. The wave 463 passes for example through a half-wave plate making it possible to align the electric field of said wave 465 with that of the wave 462. The waves 462 and 465 then pass through two holes perforated in a screen 466 before interfering with each other to form fringes on a screen 467 observed by a camera or equipped with photosensitive sensors making it possible to determine the position on said screen 467 of the brightest fringe.

[0512] Information, in particular binary type information, can be transmitted between the receivers 3 and 4 of a system 1 such as that described in [Fig. 1B], for example by following the steps illustrated in FIGS. 11A and 11B.

[0513] The correspondence protocol between the information to be transmitted, for example, between sending a bit "0" or a bit "1", and the measurement, or not, of the first photon PI, is determined before the start of the transmission.

[0514] As an example, a selection is made below consisting of not measuring the first PI photon to transmit a "0", and measuring it to transmit a "1". Of course, the opposite choice, or any other suitable correspondence, would also be valid.

[0515] In step 10, two entangled photons P1 and P2 are emitted simultaneously from an emitter 2 to receivers 3 and 4, respectively, with receiver 3 being placed closer to emitter 2 than receiver 4, as described above.

[0516] The emitted photons PI and P2 have an indeterminate quantum state in a predetermined pair of complementary polarizations, for example a 45° polarization if they are linearly polarized (the complementary polarizations being 0° and 90).

[0517] In step 11, the photon PI reaches the optical selector 30 of the receiver 3.

[0518] If a bit "0" must be transmitted, the photon PI is for example reflected by the optical selector, on a perpendicular path in the example illustrated in [Fig. 11 A] (but any other path is possible), so as not to be able to reach the measuring instrument 35. The photon PI can in particular be trapped at step 12 in a device for protecting its quantum state 5, in order to avoid its absorption, at least until the second photon P2 has reached the second receiver 4.

[0519] The PI photon, for example, retains its polarization at 45°.

[0520] If a bit "1" must be transmitted, the photon PI passes for example through the optical selector 30 to go towards the measuring instrument 35, as illustrated in [Fig. llB].

[0521] The quantum state of the photon PI is then measured by the measuring instrument 35, in step 13.

[0522] The photon PI now has a determined quantum state, for example a vertical polarization (90°), or a horizontal polarization (0°). Instantly, the measurement carried out in step 13 projects the entangled photon P2 into a determined state.

[0523] In step 15, whatever the information to be transmitted, the photon P2 reaches the optical amplifier 40 of the second receiver 4, where it is duplicated into a flow of multiplied photons P20, each photon P20 having retained the polarization of the photon P2.

[0524] In step 16, the polarization of the photon flux P20 is measured by an instrument of measure 45.

[0525] If, on average, an intermediate result is obtained, for example a polarization at 45°, it is deduced that the first photon PI has not been measured, and a bit "0" is received.

[0526] If a quantum state corresponding to a measurement in the first receiver 3 is obtained, for example a vertical (90°) or horizontal (0°) polarization, it is deduced that the first photon PI has been measured, and a bit "1" is received.

[0527] It is also possible to transmit series of discrete values ​​between the receivers 3 and 4 of a system 1 such as that described in [Fig. 1A], for example by following the steps illustrated in [Fig. 12].

[0528] In step 10, two entangled photons P1 and P2 are emitted simultaneously from an emitter 2 to receivers 3 and 4, respectively, for example with linear polarization.

[0529] In step 17, the PI photon reaches the polarization modifier 32, which converts the linear polarization of the PI photon into a selected pair of complementary polarizations, the pair having been selected according to the Jones formalism and corresponding to a discrete value to be transmitted.

[0530] In step 13, the photon PI is absorbed by the instrument 35 in one of the two complementary states of the selected pair, at the same time projecting the entangled photon P2 into its complementary state.

[0531] The following steps 15 and 17 are similar to those described above; the polarization of the photon P2 is measured by amplification then absorption, and the transmitted discrete value is deduced.

[0532] The invention is not limited to the measurement of a linear polarization of photons. Other types of quantum state can be measured and / or other measuring means can be used, in particular measurements in other observable bases.

[0533] The photons PI and P2 are for example emitted with a circular entangled polarization, and the measuring instrument 35 projects, by measuring a linear polarization, the photon PI and by entanglement the photon P2, into a linear polarization base.

[0534] Alternatively, the photons PI and P2 are emitted with a linear entangled polarization, and the measuring instrument 35 projects, by measuring a circular polarization, the photon PI and by entanglement the photon P2, according to this observable basis.

[0535] In another example, the photons P1 and P2 are emitted with a linear polarization entangled vertically or horizontally and the measuring instrument 35 measures a linear polarization at 45° or -45° from the vertical or horizontal.

[0536] In a variant, the receiver 3 comprises two measuring instruments 35, one measuring a linear polarization, the other measuring a circular polarization. The optical selector sends for example the photon PI to the first measuring instrument if a bit "1" is to be transmitted, to the second measuring instrument if a bit "2" must be transmitted, and prevents it from being measured if a "0" bit is to be transmitted.

[0537] In each of the above examples, the measuring instrument 45 of the second receiver 4 can be configured to detect whether the first photon PI has been measured, or not, and, if so, with which polarization it was measured at the first receiver.

[0538] Gyroscopes may further be used at transmitter 2 and receivers 3 and 4 to determine the polarization direction of the P1 and P2 photons, if these are emitted and transported to the receivers with linear polarization.

[0539] As mentioned above, receivers 3 and 4 as well as device 5 may be provided with devices intended to count the photons during their absorption, and optionally after they have waited for the absorption of their entangled photon, which may be accompanied by a timestamp of their arrival, as illustrated in [Fig. 13]. This may make it possible, for example, to control the correspondence between the pairs of entangled photons and the transmitted bits.

[0540] Each photon triggers for example the timestamping process by arriving at the receiver in step 80, in particular by reaching one of the measuring instruments 35 or 5D. Following this triggering event, the receiver 3 copies for example in step 82 the current time H on the clock of said receiver, for example written in a register R, on a free memory register M, preferably after having subtracted from the arrival time at the detector 5D the transit time of the photon in the waiting device 5.

[0541] A similar device (not shown) can be arranged at the second receiver 4.

[0542] Preferably, the clocks enabling the time stamping just described are syn chronologically for both receivers 3 and 4, which optionally allows defining time intervals for processing photons common to both receivers, and processing the double "multiple" pairs of photons emitted by transmitter 2.

[0543] The second receiver 4 may further comprise a switch 50 placed in front of the optical amplifier 40, and is configured to absorb or reflect the possible unwanted photon(s) PE2 which reach the receiver 4 after the photon P2 during the same processing time interval, as shown in [Fig. 14].

[0544] The switch 50 can further absorb any photons PA2 emitted by the amplifier 40 towards the emitter 2 during the amplification of the signal, or during the de-excitation of molecules or atoms from the amplifying medium.

[0545] The switch 50 is for example controlled by an electronic mechanism (not shown) itself controlled by the measuring instruments 45 when these or one of them detects photons.

[0546] In certain embodiments, the system according to the invention may comprise several transmitters arranged differently relative to the receivers, in particular in order to establish two-way communication.

[0547] In the example illustrated in [Fig. 15], the system 1 comprises two transmitters 21 and 22, each emitting pairs of entangled photons to two receivers 91 and 92.

[0548] The transmitter 21 is closer to the receiver 91 than to the receiver 92, and the transmitter 22 is closer to the receiver 92 than to the receiver 91. This arrangement allows the receivers 91 and 92 to communicate bidirectionally; the photon P11 emitted by the transmitter 21 arrives first at the receiver 91, which can then act as the first receiver 3, that is to say transmit information to the receiver 92 which receives its entangled photon P12 and acts as the second receiver 4.

[0549] Conversely, the photon P21 emitted by the transmitter 22 arrives first at the receiver 92, which this time allows information to be transmitted to the receiver 91 which receives the entangled photon P22. The mechanism for transmitting information, in particular binary information, is for example similar to what was described above, in Figures 11 and 12.

[0550] Reflecting devices 93 and 94 may be disposed near receivers 91 and 92, respectively, to reflect photons possibly reflected by receivers 91 and 92.

[0551] We will now describe with reference to [Fig. 16] an alternative implementation of the invention, intended to verify non-listening to information transmitted by the transmitter 2 and, if necessary, to generate a shared key for the exchange of information between the receivers 3 and 4, from the transfer of information that is known not to have been listened to.

[0552] The system of [Fig.16] has been modified by the addition of at least one polarizing filter 46 at the input of the receiver 4, this filter having a direction of polarization which corresponds to that expected for the photons having traveled from the transmitter to the receiver 4. The polarizing filter 46 is thus arranged upstream of the change in polarization of the photons initiated by the receiver 3 transmitting the information to the receiver 4.

[0553] The filter 46 prevents a fraudulent receiver from replacing the authentic receiver 4, from observing the exact polarization of the entangled photon after multiplication of said photon, then from emitting to the authentic receiver 4 a fraudulent photon, in replacement of the authentic photon, to be necessarily observed by the receiver 4 in the same relative polarization as the authentic photon, because on the one hand, if said photon is not entangled with another photon, its polarization will not change after passing through the filter 46 and will therefore have the polarization imposed by the filter 46 and not that of the authentic photon, and on the other hand, if the fraudulent photon is entangled with another photon called the second fraudulent photon, it is not possible to impose the relative polarization of these fraudulent photons nor moreover to destroy or stop said fraudulent photon after it has passed through the filter 46,if the verification of the relative polarization of its entangled photon is then verified as inadequate, by a third-party device.

[0554] It is therefore extremely unlikely that all or some of the photons of a group of entangled photons observed by the two receivers 3 and 4 have been observed elsewhere, if their relative polarizations are always different.

[0555] We can statistically verify the equality of the quantum state of the photons used for the transmission of information arriving at each of the two receivers 3 and 4 and deduce that the probability that some of the photons have been observed is low, by applying the following method:

[0556] When receiving photons by each of the receivers 3 and 4, the receivers note the reception time as well as the exact polarization of the photons by the use of photon detectors, and not only to which pair of complementary polarizations they belong. The times and polarizations of the detected photons too close to each other to have their polarization or arrival time measured independently are, however, preferably not noted and the two receivers 3 and 4 preferably have synchronized clocks.

[0557] After a determined number of photons carrying information I have been received, the second receiver 4 generates a message comprising the precise detection time and the polarization for each of the photons for which these attributes have been noted and having been retained as transmitting information and therefore belonging to a group of NSP photons or more having a given polarization or the complementary polarization of this polarization; NSP is defined above as the predetermined threshold number of photons received in a given polarization or its complementary polarization making it possible to identify the reception of information.

[0558] This message is signed, preferably using the random hashing technique described in application US 20210165914 A1, by the receiver 4, then is sent to the receiver 3 with said signature, preferably by implementing a quantum transmission means as described above, then the signature of the received message is verified, as well as the correspondence of the relative polarizations of the photons received by the two receivers for the pairs of photons of which the two photons have reached the receivers.This information I can be declared not to have been listened to during its transmission between the two receivers if the verification of the signature makes it appear as authentic and the proportion of polarizations not corresponding is lower than a given threshold, for example 1% if 450 pairs of different polarizations are used, or a multiple such as 2 of the probability that two pairs of different entangled photons are emitted at times indistinguishable by the receivers.

[0559] Furthermore, a relative polarization in each of the pairs of polarizations of the photons having been retained for having transmitted the information I, if this relative polarization has been verified as being different for each of the photons arriving at each of the receivers, can be used to form a sequence of bits forming a generated key randomly and known only to each of the receivers; the receiver 3 having carried out the verification of concomitance of the relative polarizations will send to the other receiver 4 a signed message, preferably by the random hashing technique, formed from the list of reception dates of the photons whose relative polarizations did not correspond or whose entangled photon was never received by the receiver 3.

[0560] Thus, in an example, the following steps are implemented.

[0561] Step 1

[0562] The receiver 4 receives, from the transmitter 2, a flow of photons carrying information and establishes a first list of the dates of reception of the photons used to determine this information as well as the relative polarization designating that of the two complementary polarizations in which the photon was received.

[0563] Step 2

[0564] The receiver 4 forms a message consisting of the list of information collected in the previous step, creates an electronic signature of this list and transmits said list as well as the signature to the receiver 3.

[0565] Step 3

[0566] Receiver 3 receives the list and the signature and then verifies said signature.

[0567] Step 4

[0568] Receiver 3 establishes a second list consisting of the elements of the first list whose relative polarizations of the photons received by receivers 3 and 4 are the same or whose entangled photon has never reached receiver 3, said receiver 3 having stored in a register the relative polarization of each photon used for the transmission of information as well as its date of reception. Knowing the difference in travel time of the entangled photons between transmitter 2 and each of the two receivers 3 and 4, that is to say the travel time, receiver 3 can determine, for each photon of the first list, the relative polarization of the photon that it received on the date of reception of the photon by receiver 4, from which the travel time has been subtracted.This second list is preferably made up of two distinct parts, a first of these parts containing photons whose entangled photon has never reached the first receiver 3 and a second of these parts containing photons whose two entangled photons have reached their respective receivers but with equal relative polarizations.

[0569] Step 5

[0570] If the number of elements of the second list limited to pairs of entangled photons of which each of the two photons has reached its respective receiver is less than the product of a predetermined ratio by the count of the elements of the first list limited to pairs of entangled photons of which each of the two photons has reached its respective receiver, then the information is declared to have been transmitted unheard.

[0571] Step 6

[0572] If the information is declared to have been transmitted unheard, then the second list is sent signed by the receiver 3 to the receiver 4, then a third list is created by the receiver 3, consisting of the relative polarizations of the photons appearing in the first list and not appearing in the second list, that is to say concerning the photons for which the relative polarizations were observed to be different.

[0573] Otherwise, that is to say if the aforementioned product is greater than said threshold, a message indicating that the transmission is likely to have been listened to is sent by the receiver 3 to the receiver 4.

[0574] Step 7

[0575] Upon receipt of the second list by the receiver 4 and after verification of the signature, the third list is recreated in the receiver 4 using the first and second lists, then a signed message, confirming the correct receipt of the second list, is sent by the receiver 4 to the receiver 3.

[0576] Step 8

[0577] Receiver 4 can use the third list as a shared key with receiver 3, and upon receipt by receiver 3 of the message transmitted in step 7, receiver 3 can use the third list as a shared key with receiver 4.

[0578] In another example, the following method may be implemented to verify that an information message I has not been listened to.

[0579] The first receiver 3 can establish a first list comprising the reception dates at the first receiver and a second list comprising these reception dates and the polarization states of the photons absorbed by the first receiver 3, and the second receiver 4 can establish a third list comprising the reception dates at the second receiver 4 and a fourth list comprising these reception dates and the polarization states of the photons received by the second receiver.

[0580] The first list and / or the third list can be exchanged between the first receiver 3 and the second receiver 4 and are preferably electronically signed.

[0581] Upon receipt of the third and / or first list, respectively, the first receiver 3 and / or the second receiver 4 may establish a fifth list comprising the dates on which the two photons of the same pairs were received at the first receiver 3, given that some photons may have been lost during transmission between the transmitter and one or both of the two receivers.

[0582] If only one of the two receivers establishes the fifth list, said fifth list can be transmitted, preferably electronically signed, to the other receiver, so that the first receiver 3 and the second receiver 4 can respectively establish a sixth list and a seventh list of polarization states of the photons as received by the first receiver, the sixth list being derived from the second list and the fifth list, the seventh list being derived from the fourth list and the fifth list, each relative polarization state, on the sixth list, of a photon received at the first receiver at a time marked on the fifth list being the same relative polarization state as that of the corresponding photon received at the same time and marked on the second list, each relative polarization state on the seventh list of a photon entangled with a photon received at the second receiver at a time marked on the fifth list being the complementary relative polarization state of the corresponding photon received after the additional travel time ttta and marked on the fourth list.

[0583] The respective signatures of the sixth list and the seventh list can then be exchanged between the first and second receivers according to the method corresponding to the third variant of the method for verifying the integrity of a message, the first receiver 3 being the first device, the sixth list being the first data set, the second receiver 4 being the second device and the seventh list being the second data set.

[0584] [Fig. 19] illustrates an example of a method for creating electronic signatures of a data set Sd. In step o, a data set, for example composed of the bits of the relative polarizations of the entangled photons PI or P2 received at the receivers 3 or 4, is created. In step i., a secret number R is concatenated to the data set to form a modified data set. In step ii., a hash of the modified data set is calculated. And in step iii., the hash is encrypted using a single-use key K, for example by an XOR operation.

[0585] Comparison of the hashes of said lists must lead to identical hashes to ensure that no list has been modified by a man-in-the-middle attack and that no photon has been lost in the transmission channel.

[0586] After these signatures have been received and verified, a signed message can be exchanged between the two receivers and said sixth and seventh lists can be used as a shared list of random bits from which, for example, one-time keys or lists of random rotation angles of the polarization measurement bases can be extracted.

[0587] In another example, illustrated in [Fig. 17], physical protection of the second propagation path D2 is used for a portion Ltot of the second propagation path D2 terminating at the second receiver 4, where the photons P2 propagate from the transmitter 2 after their entangled photons PI have been received by the first receiver 3. The portion Ltot corresponds to the sum of a smaller portion L of the portion Ltot and the additional path Ltra.

[0588] The portion Ltot is sufficiently long so that the difference t between the travel time ttot of a photon P2 in said portion Ltot and the travel time t^ of the photon P2 on the additional travel path Ltra can be detected and measured by a clock of the second receiver 4 and that this detection allows the second receiver 4 to mark any incoming message as being potentially listened to by a third party.

[0589] This prevents a hacking device placed in this unprotected portion of the propagation path from being able to listen in and retransmit the photons propagating there when they are no longer entangled.

[0590] In another example, illustrated in [Fig. 18], two polarization rotators 80 and 90 are placed upstream of the two photon receivers 3 and 4, respectively, the two photon rotators changing the polarization direction of the photons synchronously and randomly, for example by 45° or 0°, for example every photon or every other photon, so that a spy photon emitter cannot know the polarization directions measured by the receivers 3 and 4. The two receivers 3 and 4 can share a list of random bits where 0 represents a rotation of 0° and 1 a rotation of 45°.

[0591] This prevents a known secret number from being generated by a hacker replacing the entangled photon transmitter with a photon transmitter sending pairs of non-entangled photons representing a message that is also to be sent by the first receiver.

Claims

Claims

1. Method for transmitting a message M by quantum communication from a first receiver (3) to a second receiver (4) with listening detection, the transmission and detection method comprising the steps of: (A) generating a series of Np pairs of entangled photons (PI; P2) from an emitter (2), the first photon (PI) of each pair being emitted towards the first receiver (3) on a first propagation path (D1) and the second photon (P2) of the pair being emitted simultaneously towards the second receiver (4) on a second propagation path (D2), the first and second photons (PI; P2) being entangled, the second receiver (4) being located on the propagation path of the second photon (P2) further from the emitter (2) than the first receiver (3), such that the second photon (P2) arrives at the second receiver (4) after an additional travel time ttta, (B) converting the message M into a series of Ni information I to be transmitted in a first predetermined numbering base, (C) to the first receiver (3), for each information I: a. for each entangled photon (PI), modifying the polarization state of the first photon (PI) when it reaches the first receiver (3) into a polarization state dependent on the information I to be transmitted, the polarization state being selected from at least two different pairs of complementary absorption polarizations, and b. using an absorption instrument (31), absorb the first photon (PI) in one of the two complementary polarizations of the selected pair, (D) to the second receiver (4): a. duplicate each received photon (P2) into a flux of multiplied photons using an amplification device (40), the light which is created having preserved the polarization state of the photon, b. measure, for each duplicated photon, the average polarization state of the luminous flux, and c. determine according to this measurement the polarization state of the first entangled photon (PI) received by the first receiver (3), in order to deduce the information I that could have been transmitted by the first receiver (3), d. adding an element comprising the reception time of the second entangled photon and the determined polarization state of the first entangled photon which may have transmitted the information I, to a deduction list, the deduction list being a list comprising the reception times of the second entangled photons and the determined polarization states of the first entangled photons which may have transmitted the information I, (E) implement a listening detection method, (F) deducing from the deduction list the transmitted message M, the listening detection method implemented in step (E) comprising a shared quantum key generation method comprising the following steps: (G) the first receiver (3) establishes a first list comprising the dates of reception at the first receiver (3) and a second list comprising these dates of reception and the relative polarization states of the photons (PI) absorbed by the first receiver (3), and the second receiver (4) establishes a third list comprising the dates of reception at the second receiver (4) and a fourth list comprising these dates of reception and the relative polarization states of the photons (P2) received by the second receiver (4), (H) the first list and / or the third list being exchanged between the first receiver (3) and the second receiver (4), (I) upon receipt of the third list and / or the first list, respectively, the first receiver (3) and / or the second receiver (4) establish a fifth list comprising the dates on which the first photons (PI) were received at the first receiver (3), for the pairs for which the two entangled photons (PI; P2) were received at both receivers (3; 4), given that some photons may have been lost during transmission between the transmitter (2) and one or both of the two receivers (3; 4), (J) if only one of the two receivers (3; 4) establishes the fifth list, said fifth list being transmitted, preferably electronically signed, to the other receiver (4; 3), then the first receiver (3) and the second receiver (4) respectively establish a sixth list and a seventh list of relative polarization states of photons (PI) as received by the first receiver (3), the sixth list being derived from the second list and the fifth list, the seventh list being derived from the fourth list and the fifth list, each relative polarization state, on the sixth list, of a photon (PI) received at the first receiver (3) at a time marked on the fifth list being the same relative polarization state as that of the corresponding photon (PI) received at the same time and marked on the second list, each relative polarization state, on the seventh list, of a photon (PI) entangled with a photon (P2) received at the second receiver (4) at a time marked on the fifth list being the complementary relative polarization state of the polarization state of the corresponding photon (P2) received at the second receiver (4) after the additional travel time ttta and marked on the fourth list, (K) the respective signatures of the sixth list and the seventh list being exchanged between the first and second receivers (3; 4) to be compared according to a comparison method, (L) if the signatures of the sixth list and the seventh list are identical, the information deduction list I is considered to be unheard.

2. A method according to claim 1, the relative polarization of a photon (PI; P2) being the polarization of the photon (PI; P2), or a bit assigned to all possible polarizations that the second entangled photons (P2) can take after the first photon (PI) has reached the first receiver (3), where 1 is said bit assigned from an entangled photon to a photon to which a 0 has been assigned.

3. The method of claim 1 or 2, wherein the comparison method in step (K) comprises the steps of: i. mixing, at the first receiver (3), a first secret number, shared or to be shared with the second receiver (4), called a mixing number, with the sixth list, using a mixing function, in order to obtain a first mixed data, ii. hashing, at the first receiver (3), the first mixed data using a hash function, iii. encrypt, at the first receiver (3), the hash of the first data mixed with a second shared secret number or to share with the second receiver (4), iv. sending, to the first receiver (3), to the second receiver (4), the encrypted hash of the first data mixed with the second secret number, v. receiving, at the second receiver (4), the data sent by the first receiver (3) in step iv, vi. decrypting, at the second receiver (4), the received data, vii. mixing, at the second receiver (4), the first secret number with the seventh list, using a mixing function, in order to obtain a second mixed data, viii. hashing, at the second receiver, the second mixed data using a hash function, ix. comparing, at the second receiver, the hash of the second mixed data with the decrypted received data.

4. Method according to the preceding claim, the first secret number being kept secret and reused or changed periodically, for example every time or every day.

5. A method according to claim 3 or 4, the second secret number being kept secret and reused or changed periodically, for example every time or every day.

6. Method according to any one of claims 3 to 5, the first secret number being a first renewable key, renewed after each use, and / or the second secret number being a second renewable key, renewed after each use.

7. A method according to any one of claims 3 to 6, the receivers (3; 4) sharing the secret numbers before step (K) takes place or after step (K) has taken place and before their use, in particular the receivers (3; 4) sharing the secret number by sending it to each other encrypted by means of a single-use key.

8. A method according to any one of claims 3 to 7, wherein a mixer number identifier can be exchanged between the first receiver (3) and the second receiver (4), which are each capable of retrieving the corresponding mixer number from a stored list of mixer numbers.

9. A method according to any one of claims 3 to 8, the mixing function being a logical XOR function, or a suffix function, consisting of adding the mixer number to the end of the sixth list, or an encryption function using the mixer number as an encryption key to encrypt the sixth list, or the mixing function being a combination of an XOR function, a suffix function consisting of adding the mixer number to the end of the first data set and an encryption function using the mixer number as an encryption key to encrypt the first data set, the encryption function being for example an XOR function.

10. Method according to any one of claims 3 to 9, a signed message being exchanged after step ix. between the two receivers (3; 4) before the sixth and seventh lists are used as single-use keys.

11. Method according to any one of claims 3 to 10, the deduction list being considered as not having been listened to if the two data compared in step ix. are equal.

12. Method according to any one of the preceding claims, the lists established in step (G) being established for the transmission of a single information I or established using photons (PI) transmitted for the transmission of a series of multiple information I.

13. A method according to any one of the preceding claims, the second propagation path (D2) being physically protected against eavesdropping, at least for a portion (Ltot) of the second propagation path (D2) terminating at the second receiver (4), where the photons (P2) propagate from the transmitter (2) after their entangled photons (PI) have been received by the first receiver (3), the portion (Ltot) preferably being long enough so that the difference t between the travel time ttot of a photon (P2) in said portion (Ltot) and the travel time (LJ) of the photon (P2) in the non-entangled state towards the second receiver (4) can be detected by the second receiver (4) and such detection allows the second receiver (4) to mark any incoming message as potentially being eavesdropped by a third party.

14. A method according to any one of the preceding claims, two polarization rotators (80; 90) being placed before the two photon receivers (3; 4), respectively, the two photon rotators changing the polarization direction of the photons synchronously and randomly by 45° or 0° so that a spy photon emitter cannot know the polarization directions measured by the re- receivers (3; 4).

15. A method according to any preceding claim, wherein the sixth list and the seventh list are made up of bits, and can be used as a shared list of random bits.

16. A method according to any preceding claim and claim 9, the transmitted message M being used as an encryption key if the deduction list has been considered not to have been listened to.

17. Method according to any one of claims 3 to 16 and claim 9, the encryption keys generated during the transmission and detection process and / or consisting of the message M, being used if the deduction list has been considered not to have been listened to, as first and / or second secret numbers.

18. Method according to any one of the preceding claims, the first receiver (3) encoding the same information I on many successive incoming photons (PI), given that some of their entangled photons (P2) may be lost before reaching the second receiver (4), and / or the first receiver (3) reserving an information Io to be used to separate the sending of any two other information I, in particular if these two other information I are identical, representing for example the same letter.

19. A method according to any one of the preceding claims, wherein step (F), consisting of deducing the transmitted message M from the deduction list, is performed by the first receiver (3) having encoded a separator letter between any two equal successive letters of the message M, taking into account the travel time ttta and the fifth list, removing from the deduction list the photon polarizations for which the first entangled photon never reached the first receiver, in order to create an approved deduction list, and the second receiver (4) deducing the transmitted message M from the approved deduction list, or the second receiver (4) counting as received information any information successively recorded on the deduction list more than a predefined number of times within a predetermined number of successively received information I.

20. A method according to any preceding claim, the message M being considered not to have been listened to if the deduction list has been considered not to have been listened to.

21. Method according to any one of the preceding claims, the pair of complementary absorption polarizations being chosen from at least three different pairs of complementary absorption polarizations, in particular from at least 210 distinct pairs of complementary absorption polarizations.

22. Method according to any one of the preceding claims, a plurality of pairs of entangled photons (PI; P2) being generated successively by the transmitter (2), each pair of photons making it possible to transmit information I from the first receiver (3) to the second receiver (4).

23. Quantum communication system (1) implementing the method according to any one of the preceding claims, comprising: • an emitter (2) of entangled photons (PI; P2), comprising a source configured to generate at least one pair of entangled photons comprising a first photon (PI) emitted on a first propagation path (D1), and simultaneously a second photon (P2) emitted on a second propagation path (D2) different from the first propagation path (D1), • a first receiver (3) arranged on the first propagation path (D1), comprising a complex absorber (31) configured to absorb the photon (PI) in a polarization state selected from the states of at least two different pairs of complementary polarization states,• a second receiver (4) arranged on the second propagation path (D2) so as to be reached by the second photon (P2) after the first photon (PI) has reached the first receiver (3), said second receiver comprising: - an optical amplifier (40) making it possible to demultiply the second photon (P2) while retaining its polarization, and - arranged downstream of the amplifier (40), a measuring instrument (45) making it possible to measure the average polarization of the demultiplied photons.,

24. A system according to claim 23, the complex absorber (31) being configured to absorb the photon (PI) in a predetermined polarization state selected from the states of at least three different pairs of complementary polarizations.

25. System according to claim 23 or 24, the complex absorber (31) comprising: - at least one instrument (35) making it possible to absorb the photon in one or the other of two complementary polarization states, - a polarization modifier (32) which is arranged upstream of said instrument (35) and is configured to convert the polarization of the first photon (PI) into the selected polarization according to which said instrument (35) absorbs the photons.

26. System according to the preceding claim, the polarization modifier (32) comprising a polarization direction modifier (32a) arranged upstream of a polarization phase modifier (32b).

27. ​​System according to the preceding claim, the polarization direction modifier (32a) comprising two quarter-wave plates arranged one after the other on the propagation path (Dl) of the first photon (PI), the orientation of at least one of the two plates being variable.

28. A system according to claim 26, the polarization direction modifier (32a) comprising a blade or prism of chiral or rotating material inducing a rotation of the polarization by an angle depending on the location through which the wave enters said chiral or rotating material.

29. System according to any one of claims 26 to 28, the polarization phase modifier (32b) comprising a first birefringent plate or prism dividing the beam into two electromagnetic waves of linear polarization, one along a first axis and the other along a second axis, and a variable refractive index retardation plate arranged on the second axis.

30. System according to any one of claims 25 to 29, said at least one instrument (35) comprising at least one filter making it possible to send the first photon to one or the other of two photon detectors according to the polarization state of the first photon.

31. System according to any one of claims 23 to 30, the measuring instrument (45) of the second receiver (4) comprising at least at least one photon detector (455) arranged to measure the polarization of the light resulting from the multiplication of the second photon (P2).

32. System according to any one of claims 23 to 31, the measuring instrument (45) of the second receiver (4) comprising a succession of semi-reflecting plates (452) arranged downstream of the optical amplifier (40), said plates (452) directing the flux of photons multiplied with equal intensity towards a first phase measuring instrument, the latter being a polarization measuring instrument arranged to measure the intensity of the flux along two perpendicular axes, a second phase measuring instrument measuring the phase shift of the light between these same two axes, and a third phase measuring instrument measuring the phase shift of the light between the bisector of the same axes and an axis perpendicular to this bisector, the first semi-reflecting plate deflecting for example a third of the luminous flux towards the first phase measuring instrument,the second semi-reflecting blade deflecting for example half of its incoming light flux towards the second phase measuring instrument and the remaining half of its incoming light flux towards the third phase measuring instrument.,

33. A system according to any one of claims 23 to 32, the optical amplifier (40) being a doped fiber amplifier.

34. System according to any one of claims 23 to 33, the transmitter (2) being configured to successively generate a plurality of pairs of entangled photons (PI; P2).

35. System according to any one of claims 23 to 34, the transmitter (2) and each of the receivers (3; 4) comprising a clock, the clocks of the transmitter (2) and the receivers (3; 4) being synchronized with each other.

36. System according to any one of claims 23 to 35, the second receiver (4) comprising a switch (50) arranged in front of the optical amplifier (40) and configured to absorb or reflect the photon(s) subsequent to a first photon reaching said second receiver (4) within a predetermined time interval.

37. A system according to any one of claims 23 to 36, comprising a second transmitter capable of generating one or more pairs of entangled photons, the second transmitter being located closer to the second receiver (4) than to the first receiver (3).

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