TRANSMISSION OF A MESSAGE VIA QUANTUM COMMUNICATION WITH ETCHING DETECTION

Description

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. Previous technique Cryptography

[0002] Computers and electronic devices are often connected to a network, physically, wirelessly, by RFID, or by any other secure or unsecure means, and sometimes need 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 legitimate recipient, or simply to identify without a shadow of a doubt the identity of the sender of the data, which is for example a car 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 Generator Device (QKD), or for any other reason why the identity of the sender of the data is important to the recipient.

[0003] Quantum key generation 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 the electronic signature of received keys, thus allowing the supposedly secret key to be shared between a legitimate device and an illegitimate device without the legitimate device being aware of it.

[0004] The transmitted data can be sent fully encrypted using a key assigned to the sender. However, fully encrypting the data makes it difficult to use one-time keys (block keys). More specifically, fully encrypting the data is a process 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 encrypting a smaller amount of data than the amount of data sent. This is why an electronic signature is used, consisting of encrypting a hash of the data. The term "hashing" refers to the result of a hash function which, based on initial input data, calculates a fingerprint used to quickly, though incompletely, identify the initial data. It is common practice to send an encrypted hash along with the data, which is then decrypted by the recipient and compared to the hash of the received data.MD5, SHA1, and SHA256 are commonly used algorithms for hashing. However, data hashes are generally much smaller than the original data, and it may be possible to create alternative data, similar but slightly different from the original, whose hash matches the original data's hash. This data could then 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's detectability of the substitution decreases as the data's complexity 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.Furthermore, hash functions such as MD5 and SHA1 are hash functions that are currently relatively easy to bypass.

[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 so 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 data fragment 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 hash result 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. The failure to encrypt the hash when the message itself is not encrypted makes the transmission vulnerable to very powerful or quantum computers capable of calculating random numbers compatible with both the unencrypted message and the hash result. Furthermore, encrypting the entire message has the drawback, if this encryption uses one-time block keys, which are supposed to be unbreakable, of requiring both corresponding parties to have access to these shared keys. Quantum communication

[0011] Information transmission is currently done primarily through electromagnetic waves, whether these have short wavelengths, like light, or long wavelengths like VHF waves.

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

[0013] These methods use wave propagation to transmit energy and therefore physical particles which, collected by a receiver, allow information to be deduced, which is coded, for example, by their wavelength or by modulation of the duration of 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 instance, via an optical fiber. The value of a bit is arbitrarily assigned to a direction, or a polarization mode, of the photon. Sequences of polarized photons can then be sent to transmit binary sequences that make up a message.

[0016] In quantum cryptography, it is well known to use a pair of entangled photons to transmit information securely. Entangled photons are photons whose quantum states, such as their polarization, are interdependent regardless of the distance separating them.

[0017] This quantum entanglement phenomenon 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 µm" (Sci Adv, 2020).

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

[0019] Wang's article, "Superluminal telecommunication: an observable contradiction between quantum entanglement and relativistic causality," reveals a quantum communication system enabling superluminal information transmission through a pair of entangled photons sent to two receivers wishing to communicate. 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 multiplied, and the average polarization of the multiplied flux is measured to determine the direction in which the first photon was measured.

[0020] The polarization of a photon is not necessarily binary like that of a spin or even quaternary. It can notably be represented on the Jones sphere which characterizes the orientation and ellipse of the polarization: a polarization can indeed 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.

[0021] 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.

[0022] The aforementioned devices do not allow the exploitation of all polarization configurations and are therefore limited in the number and type of information that can be transmitted.

[0023] The ITU Telecommunication standardization sector document "Draft D2.3 Technical Report on quantum key distribution network (QKDN) protocols part 1: Quantum layer (output of 9th FG-QIT4N meeting" (August 17, 2021) discloses a method for transmitting a message by quantum communication from a first receiver to a second receiver with eavesdropping detection. Description of the invention

[0024] There is a need to further refine quantum communication systems and processes in order to take advantage of entangled photons and to prevent and detect eavesdropping during entangled photon communication. Summary of the invention

[0025] The invention aims to meet this need and achieves this, according to one of its aspects, through a method of 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 of: (A) generate a series of N p pairs of entangled photons from an emitter, 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 emitter than the first receiver, such that the second photon arrives at the second receiver after an additional travel time ttra, (B) convert the message M into a series of N i information I to be transmitted in a first predetermined numbering base, (C) at the first receiver, for each information I: (a) for each entangled photon, modify the polarization state of the first photon when it reaches the first receiver to a polarization state dependent on the information I to be transmitted,(a) 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, (D) at the second receiver: (a) duplicate each received photon into a stream of multiplied photons by means of an amplification device, the light that is created having preserved the polarization state of the photon, (b) measure, for each duplicated photon, the average polarization state of the light stream, and (c) determine from this measurement the polarization state of the first entangled photon received by the first receiver, in order to deduce the information I that may have been transmitted by the first receiver, (d) add an element including the reception time of the second entangled photon and the determined polarization state of the first entangled photon that may have transmitted the information I, to a deduction list,the deduction list being a list containing the reception times of the second entangled photons and the determined polarization states of the first entangled photons that may have transmitted the information I, (E) implement a listening detection method, (F) deduce from the deduction list the transmitted message M, , the eavesdropping detection method implemented in step (E) comprising a shared quantum key generation method including the following steps: (G) the first receiver establishes a first list containing the dates of reception at the first receiver and a second list containing these dates of reception and the relative polarization states of the photons absorbed by the first receiver, and the second receiver establishes a third list containing the dates of reception at the second receiver and a fourth list containing these dates of reception and the relative polarization states of the photons received by the second receiver, (H) the first list and / or the third list being exchanged between the first receiver and the second receiver, (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 containing 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 both receivers,given that some photons may have been lost during transmission between the transmitter and one or both of the two receivers, (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 establish respectively 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 and fifth lists, the seventh list being derived from the fourth and fifth lists, 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 complementary relative polarization state of the polarization state of the corresponding photon received at the second receiver after the additional travel time ttra 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 to be compared according to a comparison procedure, (L) if the signatures of the sixth list and the seventh list are identical, the information inference list I is considered to be unlistened.

[0026] The relative polarization of a photon can 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 can take after the first photon has reached the first receiver, where 1 is said bit assigned from an entangled photon to a photon to which a 0 has been assigned.

[0027] The comparison process at step (K) may include the following steps: i. Mix, at the first receiver, a first secret number, shared or to be shared with the second receiver, called the mixer number, with the sixth list, using a mixing function, in order to obtain a first mixed data, ii. Hash, at the first receiver, the first mixed data using a hash function, iii. Encrypt, at the first receiver, the hash of the first mixed data with a second secret number shared or to be shared with the second receiver, iv. Send, from the first receiver, to the second receiver, the encrypted hash of the first mixed data with the second secret number, v. Receive, at the second receiver, the data sent by the first receiver in step iv, vi. Decrypt, at the second receiver, the received data, vii. Mix, 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.hash, 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 received decrypted data.

[0028] The first secret number can be kept secret and reused. Preferably, the first secret number can be changed periodically, for example, every time or every day.

[0029] The second secret number can be kept secret and reused or, preferably, can be changed periodically, for example every time or every day.

[0030] The first secret number can be a first renewable key, for example renewed after each use and / or the second secret number can be a second renewable key, for example renewed after each use.

[0031] Preferably, the first secret number is kept secret and reused, and the second secret number is a one-time use key renewed after each use.

[0032] The transmission and detection process is preferably not implemented if the first or second key is no longer secret.

[0033] The receivers can share the secret numbers between themselves before step (K) takes place. Alternatively, the secret numbers can be exchanged between the two receivers after step (K). The receivers can share the secret number by sending it to each other encrypted using a one-time key.

[0034] A mixer number identifier can 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.

[0035] The shuffler function can be a logical XOR function, or a suffix function, consisting of adding the shuffler number to the end of the sixth list, or an encryption function using the shuffler number as the encryption key to encrypt the sixth list.

[0036] The mixing function can alternatively be a combination of an XOR function, a suffix function consisting of adding the mixing number to the end of the first dataset, and an encryption function using the mixing number as the encryption key to encrypt the first dataset.

[0037] The encryption function can be an XOR function.

[0038] A signed message can be exchanged after step ix between the two receivers before the sixth and seventh lists are used as one-time keys.

[0039] Information deduction list I can be considered as not having been listened to if the two data compared in step ix. are equal.

[0040] The lists established in step (G) can be established for the transmission of a single piece of information I. Alternatively, the lists established in step (G) can be established using transmitted photons for the transmission of a series of multiple pieces of information I.

[0041] The second propagation path is preferably physically protected against eavesdropping, at least for a portion of the second propagation path terminating at the second receiver, where photons propagate from the transmitter after their entangled photon has been received by the first receiver. This prevents a hacking device placed in this unprotected portion of the propagation path from eavesdropping and retransmitting the photons propagating there when they are no longer entangled. This portion is preferably long enough so that the difference between the travel time of a photon in this portion and the travel time of the photon in its unentangled state to the second receiver can be detected by the second receiver, and this detection allows the second receiver to flag any incoming message as potentially being intercepted by a third party.

[0042] Two polarization rotators are preferably placed in front of the two photon receivers, respectively. These two rotators change the polarization direction of the photons synchronously and randomly, for example by 45° or 0°, for example by every photon or every other photon, so that an eavesdropping photon emitter 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.

[0043] This prevents a known secret number from being generated by a hacker who would replace the entangled photon emitter with a photon emitter sending pairs of non-entangled photons representing a message that is also meant to be sent by the first receiver.

[0044] The sixth and seventh lists can be made up of bits, and can potentially be used as a shared list of random bits.

[0045] The transmitted message M can be used as an encryption key if the deduction list was deemed not to have been listened to.

[0046] The encryption keys generated during the transmission and detection process and / or consisting of the message M, can be used if the deduction list was considered not to have been listened to, as the first and / or second secret numbers.

[0047] The first receptor can encode the same information I on many successive incoming photons, since some of their entangled photons may be lost before reaching the second receptor.

[0048] The first receiver can reserve an information I 0 to be used to separate the sending of any two other pieces of information, especially if these two other pieces of information are identical, representing for example the same letter.

[0049] Step (F), consisting of deducing the transmitted message M from the deduction list, can be carried out by the first receiver having encoded a separation letter between any two successive equal letters of the message M, taking into account the travel time t tra 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 deducing from the approved deduction list the message M having been transmitted.

[0050] Alternatively, the second receiver can 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 pairs of different polarization states that can be encoded on photons and if the propagation paths lose 90% of the photons between the emitter and the receivers, the second receiver can 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 recordings of the deduction list.

[0051] Message M can be considered not to have been listened to if the deduction list was considered not to have been listened to.

[0052] The pair of complementary absorption polarizations can be chosen from at least three different pairs of complementary absorption polarizations.

[0053] The pair of complementary absorption polarizations can be selected from at least 210 distinct pairs of complementary absorption polarizations.

[0054] A plurality of entangled photon pairs can be generated successively by the emitter, each pair of photons allowing information to be transmitted from the first receiver to the second receiver. First quantum communication system

[0055] According to another aspect, the invention relates to a first quantum communication system implementing the process described above, comprising: an entangled photon emitter, 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 disposed 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 disposed 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 enabling the second photon to be multiplied while preserving its polarization, and ∘ disposed downstream of the amplifier,A measuring instrument that allows the measurement of the average polarization of multiplied photons.

[0056] The complex absorber can be configured to absorb the photon in a predetermined polarization state selected from the states of at least three different pairs of complementary polarizations.

[0057] The complex absorber may include: at least one instrument capable of absorbing the photon in either 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 in which said instrument absorbs photons.

[0058] The polarization modifier may include a polarization direction modifier arranged upstream of a polarization phase modifier.

[0059] The polarization direction modifier may include 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.

[0060] The polarization direction modifier may include a blade or prism of chiral or rotating material inducing a rotation of the polarization by an angle dependent on the location through which the wave enters said chiral or rotating material.

[0061] The polarization phase modifier may include a first birefringent plate or prism dividing the beam into two linearly polarized electromagnetic waves, one along a first axis and the other along a second axis, and a variable refractive index retarder plate arranged on the second axis.

[0062] Said at least one instrument may include at least one filter enabling the first photon to be sent to one or the other of two photon detectors depending on the polarization state of the first photon.

[0063] The measuring instrument of the second receiver may include at least one photon detector arranged to measure the polarization of the light resulting from the multiplication of the second photon.

[0064] The measuring instrument of the second receiver may comprise a succession of semi-reflective plates arranged downstream of the optical amplifier, said plates directing the flux of multiplied photons 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.

[0065] The first semi-reflective blade can deflect one third of the light flux towards the first phase measuring instrument, and the second semi-reflective blade can deflect 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.

[0066] The optical amplifier can be a doped fiber amplifier.

[0067] The emitter can be configured to successively generate a plurality of entangled photon pairs.

[0068] The transmitter and each of the receivers may include a clock, with the clocks of the transmitter and receivers being synchronized with each other.

[0069] The second receiver may include a switch disposed 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.

[0070] The first quantum communication system may include a second emitter 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. Second quantum communication system

[0071] The invention also relates to a second variant of a quantum communication system according to the invention, comprising: an entangled photon emitter, 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 disposed 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, with the exception of 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 preserving its polarization and, arranged downstream of the amplifier, a measuring instrument allowing the average polarization of the multiplied photons to be measured.

[0072] The second variant of the system according to the invention is arranged to transmit almost instantaneously a series of values, continuous or discrete, between two locations.

[0073] Since the first and second photons are entangled, the absorption of the first photon at the first receptor instantly determines the polarization of the second photon, especially before it reaches the second receptor.

[0074] Measuring the average polarization of the multiplied photons at the second receiver then makes it possible to detect in which polarization state the first photon was absorbed and to deduce the transmitted information.

[0075] 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 very little energy.

[0076] The second variant of the system is used for example for communication and computer networks on Earth, in the sky and / or in space, in particular to communicate with systems far from Earth, such as satellites or spacecraft. Jones' Polarizations

[0077] By "complementary polarization states", also referred to hereafter as "complementary absorption polarization states", we mean 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 one of them to be absorbed by a first polarizing filter, and the other to be absorbed by a second polarizing filter with a polarization orthogonal to that with which the first polarizing filter can absorb.

[0078] In the following, the terms "polarization state" and "polarization" are used interchangeably.

[0079] The first receiver is advantageously arranged so that its user can select the polarization state in which the photon is absorbed from among any of the possible polarizations as defined by the Jones formalism, in particular from among a set of elliptic (also called "ellipsoidal") polarizations characterized by the orientation and ellipse of the polarization.

[0080] This allows us to vary the polarization according to which photons are absorbed by the first receptor in order to transmit a series of information to the second receptor.

[0081] By selecting, for example, 10 different polarization directions, spaced 9° apart, and 21 different phase shifts, also spaced 9° apart, we can define 210 different polarization states and thus transmit 210 different signals.

[0082] For example, we can transmit the letters of the alphabet in uppercase, lowercase, numbers and a number of other special characters, for each of the pairs of entangled photons reaching the receptors. Complex absorber

[0083] A "complex absorber" is defined as a set reached by the first photon which allows a pair of complementary polarizations to be determined from among a number of complementary polarization pairs, and which absorbs the first photon in one of the two polarization states of the predetermined pair.

[0084] 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.

[0085] Preferably, the complex absorber comprises: at least one absorption instrument capable of absorbing the photon in either 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 photons.

[0086] By "selected polarization", we mean a pair of complementary polarizations predetermined according to the information to be transmitted. Polarization modifier

[0087] The linear polarization of a photon can be converted into ellipsoidal polarization as represented by the Jones formalism by first modifying the orientation of the polarization of a photon of linear polarization and known direction, thus distributing the electric field in a predetermined way along an x-axis and a y-axis perpendicular to the x-axis and then, secondly, by modifying the phase of the electric field along one of two perpendicular directions, for example the y-axis.

[0088] The polarization modifier preferably includes a polarization direction modifier arranged upstream of a polarization phase modifier.

[0089] For example, if θ is the rotation angle of the linear polarization and ϕ the phase shift along the y-axis, ω being the angular frequency of the wave, the components Ex And E y The electric field strengths after rotation are: E x = E Cos θ Cos ωt E y = E Sin θ Cos ωt

[0090] And after the phase shift: E x = E Cos θ Cos ωt E y = E Sin θ Cos ωt + ϕ Polarization direction modifier

[0091] 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.

[0092] The polarization direction modifier may include 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.

[0093] The first quarter-wave plate, for example, modifies the linear polarization into circular polarization, and the second quarter-wave plate, for example, converts 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.

[0094] Rotating the axis of this second plate allows the direction of the photon's linear polarization to be changed. If the plate is a half-wave plate, rotating it also allows the direction of the photon's linear polarization to be changed.

[0095] Alternatively, one can change the orientation of the first quarter-wave plate, while that of the second remains fixed, or one can change the orientations of both quarter-wave plates.

[0096] The rotation of a quarter-wave blade or a half-wave blade is obtained, for example, by mechanical control to a sensor or an electrically controlled device enabling 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.

[0097] Alternatively, a plurality of linear polarization rotation devices can be used, each allowing different rotation angles, for example fixed, but equally able to be modified, selectors allowing the photons to be sent to one of these rotation devices and, at the output of said rotation device, to be conducted to a common waveguide or common transmission axis.

[0098] These selectors may include a mirror whose axis direction is controlled, for example, by an electrical device, or alternatively consist of a prism or a plate 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 luminous flux, for example transverse and preferably of a wavelength different from that of the photon and unable 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 exit direction of the photon of said material.Since the rotational inertia of a quarter-wave plate can be significant, photons can be sent successively to different quarter-wave plates whose direction has been adjusted beforehand, for example by one of the mechanical rotation devices described previously, thus allowing time to change the direction of each of these quarter-wave plates between two photon passes.

[0099] Alternatively, chiral or rotating materials can be used to modify a linear polarization direction.

[0100] The polarization direction modifier may include a plate or prism made of chiral or rotating material that induces a rotation of the polarization by an angle dependent on the point at which the wave enters said chiral or rotating material. The material may, in particular, be arranged between two Pockels cells.

[0101] The first photon can be projected onto a first plate or prism forming a Pockels cell whose refractive index is controlled by an electric field to emerge at different locations, notably onto an intermediate plate or prism of material at least partly chiral or rotating, rotating the axis of electric polarization of the photon by an angle depending on the location through which the wave enters said intermediate plate or prism, before entering a second plate or prism forming a Pockels cell whose refractive index is adjusted symmetrically with respect to that of the first plate or prism to make the photon 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 blade whose refractive index can be adjusted, for example electrically, is advantageously placed after the second blade or prism to allow the location of the photon exiting the assembly of blades and prisms to be independent of the refractive index selected for the first blade or prism.

[0102] The intermediate material plate or prism is for example composed of two symmetrical prisms joined together with the same refractive index but having different chiral or rotational powers, the first of the two prisms having for example a chiral or rotational power and the second not having one or rotating the electric field in the opposite direction to the rotation imposed by the first prism.

[0103] One of the two intermediate prisms may contain a chiral material, for example cadmium selenide (CdSe) nanoparticles with a diameter of approximately 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 having the opposite chirality to that of said first intermediate prism. Since the rotation of the electric field of waves passing through a chiral material is 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.

[0104] One of the two intermediate prisms may further include a "rotating" material, such as a superposition of an even number of quarter-wave plates stacked one on top of the other in directions incremented at each layer by a predetermined angle, such that a wave polarized linearly along the axis of the first slice of material emerges from the stack with a polarization rotated by an angle proportional to the thickness of the stack. Polarization phase modifier

[0105] A second device, called a "polarization phase modifier", can be placed downstream of the polarization direction modifier, in order to phase shift the electric field component of the photon by a predetermined angle along one of two fixed axes.

[0106] Preferably, the polarization phase modifier comprises a first birefringent plate or prism arranged to split the beam into two linearly polarized electromagnetic waves, one along a first axis, the other along a second axis, and a retarding plate having a variable refractive index arranged on the second axis.

[0107] By "beam", we must understand the light wave which is the first photon in the sense of the duality of light.

[0108] 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 again by a new plate or a new birefringent prism allowing the two waves whose polarization fields are perpendicular to be joined along the same axis.

[0109] The delay plate can incorporate a Pockels cell or a nonlinear material. The variable refractive index allows selection of the phase shift imposed on the wave oriented along the second axis.

[0110] In a first implementation example, as described above, the phase modifier rotates a linear polarization by 9° intervals between -45° and +36° and varies the phase by 9° intervals between -90° and +90°, thus defining 210 possible polarization states. As described below, 209 of the 210 possible polarizations are used, for example, 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 used to encode data.

[0111] In a second implementation example, 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

[0112] The invention also relates to a third variant of the quantum communication system according to the invention, comprising: an entangled photon emitter 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 disposed 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 indeterminate in the observable basis according to which the first instrument absorbs the photons, an optical selector disposed upstream of said at least one first instrument and configured to either allow the first photon to pass to said at least one first measuring instrument, or to 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 allowing the second photon to be multiplied while preserving its polarization and, arranged downstream of the amplifier, a measuring instrument allowing the average quantum state of the multiplied photons to be measured.

[0113] By "observable basis" we mean a basis of two complementary polarizations, for example two orthogonal linear polarizations.

[0114] By "indeterminate polarization in an observable basis", we mean 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 way.

[0115] Since the first and second photons are entangled, the absorption of the first photon at the first receptor instantly determines the polarization of the second photon, especially before it reaches the second receptor.

[0116] Measuring the polarization of the multiplied photons at the second receiver then allows us to detect whether the first photon was absorbed or not, and to deduce what information was transmitted. The information transmitted by this third variant of the system is, for example, binary.

[0117] The first receiver may include at least one second absorption instrument, the optical selector being positioned upstream of the first and second instruments and configured to either allow the first photon to pass through by directing it towards one or the other of the instruments, or to prevent it from being absorbed.

[0118] Using two instruments allows three different pieces of information to be transmitted, for example the values ​​0, 1 and 2, with the value 0 being assigned to reflection, the value 1 to the first instrument, and the value 2 to the second instrument. Optical selector

[0119] The optical selector of the first receiver can be of various types. It is advantageously placed upstream of the measuring instrument so as to prevent the incident photon from reaching the measuring instrument, if desired.

[0120] To achieve this, the selector preferably includes a reflector, in particular a controlled mirror, allowing for example to reflect the first photon onto a propagation path different from its incident propagation path, in particular onto a propagation path not containing the measuring instrument.

[0121] By "controlled mirror" we mean a device whose properties, for example the properties of refraction or the direction of reflection, are controlled by an auxiliary device connected to the mirror, in particular an electronic device, for example generating an electric field.

[0122] The optical selector preferably includes a device whose refractive index and / or direction of reflection are controlled, in particular controlled by means of an electric field or a luminous flux.

[0123] Alternatively, the optical selector includes, for example, a Bragg mirror, in particular a Bragg mirror whose reflection direction is controlled by a piezoelectric material, itself controlled by an electric field.

[0124] Alternatively, the optical selector includes 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 with respect to the direction of incidence of the electromagnetic waves reaching it, so that said waves are reflected towards a place preferably different from that from which they come at the entrance of the prism.

[0125] In another variant, the optical selector comprises one or a succession of Bragg filters, some layers of which are Pockels cells whose refractive index is controlled by an electric field, the said Bragg filter reflecting or letting through the light wave depending on whether or not the electric field is applied.

[0126] Alternatively, the Pockels cells used above are replaced by nonlinear crystals illuminated by a powerful light that can vary the refractive index of the medium through which the photon passes, the wavelength of the powerful light preferably being different from the wavelength of the photon.

[0127] The optical selector allows, in particular, the orientation of photons in three different directions: one direction allowing, for example, that photons not be detected, a second allowing the measurement of a linear polarization of photons, and a third allowing the measurement of a circular polarization. Protective device

[0128] 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 that prevents the measurement or absorption of at least one photon, disposed near the first receiver so as 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.

[0129] 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 observed there, i.e. when it is not desired that it be absorbed by the measuring instrument of the first receiver.

[0130] Preferably, the quantum state protection device includes 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.

[0131] Preferably, it comprises a plurality of Bragg mirrors, arranged with respect to the transparent space so as to trap the photon it receives on a path of appropriate length, as described above, i.e. corresponding to the time it takes for the second photon having reached the second receiver to be amplified there.

[0132] Alternatively, the protection device includes an optical fiber of sufficient length to allow the first photon to travel through it while waiting for the second photon, having reached the second receiver, to be amplified there.

[0133] In another variant, the device can be a portion of empty or gas-filled space or atmosphere which is ensured is not traversed by an object reflecting or absorbing light. First photon absorption instrument

[0134] At the first receiver, the first photon can be absorbed by at least one absorption instrument in one of two states of a pair of complementary polarizations.

[0135] Preferably, the absorption instrument includes at least one filter enabling the first photon to be sent 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 plate of birefringent material.

[0136] The absorption instrument may also include a polarizing filter and a photon detector located after said polarizing filter.

[0137] The absorption instrument may also include a semi-transparent mirror reflecting circularly polarized photons towards a first photon detector and allowing others to pass to a second photon detector, as described in the May article, Wending, et al. "Broadband transparent chiral mirrors: Design methodology and bandwidth analysis." ( AIP Advances 9.4 (2019): 045305). Emission of photons Photon pair emitter

[0138] Preferably, the emitter generates entangled photon pairs by spontaneous parametric frequency lowering (SPDC), i.e. by a process in which an initial photon, also called the "pump" photon, is split and its frequency divided by two by a four-wave mixing phenomenon, in an optical medium with a nonlinear refractive index, as described in the article by Amanti et al., "Integrated sources of entangled photons at the heart of quantum technologies" (Photonics, issue 91, 2018).

[0139] This type of photon pair emitter produces photons with relatively robust entanglement, but has the disadvantage of sometimes producing more than one photon pair at a time, which is undesirable because it is uncontrolled. Auxiliary devices can be implemented to handle these "parasitic" multiple pairs, as described below.

[0140] Alternatively, an emitter incorporating a quantum dot can be used to generate entangled photon pairs, as described in the aforementioned article, which allows for more regular pair formation. However, the entanglement properties of photons obtained using such a method can sometimes be unstable.

[0141] 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).

[0142] Preferably, the emitter is configured to successively generate a plurality of entangled photon pairs.

[0143] The entangled photons at the emitter output can be sent along the first and second propagation paths in various ways. Broadcast according to a predetermined polarization

[0144] Photons are preferably emitted with a predetermined polarization. By "predetermined polarization," we mean in one of the two states of a predetermined pair of complementary polarizations, for example, a linear polarization in a certain direction. A birefringent plate can, for example, separate the two entangled photons according to their vertical or horizontal linear polarization.

[0145] A predetermined polarization of the entangled photons sent to each of the receptors makes it possible to know the probability of a state according to a polarization or its complementary polarization for any selected pair of complementary polarizations.

[0146] We can thus 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 complementary polarization of the polarization observed at the first receiver.

[0147] A predetermined polarization is also necessary when using quarter-wave plates at the first receiver to rotate the polarization direction of the first photon.

[0148] To emit photons according to a predetermined linear polarization, a blade or prism containing an optically transparent birefringent material, for example lithium niobate or rutile (TiO2), is placed at the output of the emitter, whose optical indices depend on the axis of polarization of the light through which at least one of the two photons passes.

[0149] This photon then exits the prism at one of two different locations, depending on its linear polarization.

[0150] 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 point where the electromagnetic waves whose electric field is parallel to the ordinary axis of the optically transparent birefringent material emerge, to send it to the first receiver.

[0151] Similarly, the second photon exiting from the point where electromagnetic waves whose field is perpendicular to the ordinary axis emerge is collected in order to send it towards the second receiver.

[0152] 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 prism and each photon redirected to its intended receiver, the photons exiting from different locations of the prisms then being preferably lost or destroyed by projection onto an absorbing surface.

[0153] For example, we can use for the first entangled photon the one coming out of a first birefringent plate or a first birefringent crystal with a linear polarization parallel to the first axis, and as the second entangled photon the one coming out 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 photons entangled with the photons coming out of the first plate or the first birefringent prism in a direction parallel to the first axis.

[0154] To facilitate the transport of said photons to the receivers, birefringent delay plates are preferably placed at the exit of the places where the photons come out of the prisms, converting the linear polarizations of said photons into circular polarization.

[0155] We then preferably have another birefringent delay plate at the entrance of each of the receivers to convert the circular polarizations of the photons into linear polarization, this conversion into linear polarization allowing the polarization axis to be precisely adjusted. Transmission of photons

[0156] Photons can be transmitted from emitters to receivers through space, through the atmosphere, via optical fiber, or a combination of these means.

[0157] Lenses can be used for photon transmission, particularly for transmission through space or the atmosphere. If necessary, anti-reflective coatings are preferably applied to these lenses. The size of the lenses used is preferably adapted to the length of the spatial or atmospheric transmission of the photons.

[0158] Conjugate mirrors, which reflect the emitted light back to the emitter, can be used to adjust the emission direction of conjugated photons for spatial or atmospheric transmission. For example, a laser light emitter can scan a space to detect the receiver, which then reflects the emitted light back to it. The direction of the conjugated photons is then adjusted to be parallel to, or coincide with, the direction of the light reflected by the conjugate mirrors.

[0159] The light emitted by the laser light emitter can be of a wavelength close to the wavelength of the entangled photons and be introduced by a dichroic prism into the lens used by the photons.

[0160] Alternatively, if the wavelength is the same as that of the entangled photons, the light can be introduced through a birefringent prism when these photons are linearly polarized. The polarization of the guiding light is then 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 upon the arrival of the guiding light.

[0161] 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.

[0162] In another variant, one may not use a conjugate mirror but still aim at the receivers or targets close to them, the information that the targets are received being communicated by another means of communication, in particular by radio signal or by quantum transmission.

[0163] The area to be explored can be identified by mapping the area in which said receivers are likely to be located.

[0164] The aforementioned phase modifier can also be used when the receivers are in relative rotation with respect to the emitter, particularly due to the rotation of the Earth or satellites, to allow photons emitted in a fixed direction with respect to the emitter to enter each of the receivers with a fixed and determined direction with respect to it. Calibration methods

[0165] The various media through which photons pass from their point of emission to the two receivers can give rise to modifications of their phase that are not necessarily desired or expected.

[0166] Furthermore, these modifications can differ depending on whether the photons are directed towards the first or second receptor. Finally, these modifications can vary over time, depending in particular on the weather or the temperature of the materials during their use.

[0167] The system according to the invention can be periodically calibrated by having the first receiver absorb photons in polarizations belonging to predetermined pairs of complementary polarizations and observing for each of these pairs one of the two possible polarizations in which the entangled photon is detected by the second receiver.

[0168] Thus, the invention also relates to a calibration method for a system as defined above, enabling the determination of the polarization state of a photon reaching the second receptor as a function of the polarization state in which its entangled photon was absorbed at the first receptor, a method comprising the steps of: generate 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 the one of the two possible polarizations in which each photon was absorbed and stop sending photons from the emitter as soon as a predetermined number of each of the different polarizations have been observed, at the second receiver, duplicate the second photons into multiplied photon streams by means of 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 multiplied photon stream,and store these measurements along with their reception times, transmit the list of polarizations and reception times of the stored photons from the first receiver to the second receiver, remove from the list of photons received at the second receiver the photons that do not correspond to photons received at the first receiver and, similarly, remove from the list of photons received at the first detector the photons whose corresponding photon was not received at the second receiver, and calculate, using on the one hand: the knowledge of the polarization state of two photons detected in polarizations complementary to the first receiver and whose entangled photons reached the second receiver, and on the other hand the knowledge of the polarization state of the corresponding entangled photons received at the second receiver, the Jones matrix allowing the polarization of the photons received at the second receiver to be deduced from the polarization of the photons received at the first receiver.

[0169] The storage of states as well as the calculation of the Jones matrix can be carried out by any suitable electronic device, for example a microcontroller.

[0170] The Jones matrix thus calculated allows the polarization of the second entangled photon received at the second receptor to be calculated as a function of the absorption polarization of the first photon by the complex absorber located at the first receptor.

[0171] 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 complementary polarization pairs 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.

[0172] Thus, the invention also relates to a calibration method for a system as defined above, enabling the determination of the probability of losing a photon during its transit from the emitter to the first receiver, consisting of: configure the complex absorber of the first receiver to absorb the photons received at the first receiver in one of two complementary polarizations of a pair of absorption polarizations, successively generate 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 polarization state, count the number of photons received at the second receiver in each of the ranges of polarizations detectable by the second receiver other than one of the two ranges of polarizations of the entangled photons of the photons absorbed by the first detector.

[0173] We can thus detect ranges of polarizations in which entangled photons of lost photons during transmission on their way to the first detector arrive first, or most likely, and thus preferably avoid using the corresponding absorption polarizations to transmit data from the first to the second receiver.

[0174] We can also, by taking the quotient between the number of photons received at the second receiver according to one of the polarizations corresponding to one of the two absorption polarizations at the first receiver, calculate a photon transmission ratio between the emitter and the second receiver. Second receiver measuring instrument

[0175] The measuring instrument of the second receiver preferably includes at least one photon detector arranged to measure the polarization of the light resulting from the multiplication of the second photon.

[0176] The measuring instrument of the second receiver includes, for example, a series of semi-reflective plates arranged downstream of the optical amplifier, said plates 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 two same axes.

[0177] Light can also be directed to various polarizing filters after passing through one or a succession of lenses that enlarge the cross-section of the light beam, thus allowing a plurality of mirrors or lenses to direct portions of this light beam to the various polarization measuring instruments.

[0178] The various polarization measurement instruments preferably allow for: measure the intensity of the component of the electric field of light along a first x-axis, measure the intensity of the component of the electric field of 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.

[0179] The measurement of light intensity along two perpendicular axes is carried out, for example, by splitting the light along two perpendicular axes using a birefringent plate or prism, followed by two light intensity sensors placed at the outputs of said plate or prism. The measurement of the phase difference between two perpendicular components is carried out, for example, by splitting the light along two perpendicular axes using a birefringent plate or prism, followed, for the wave polarized along one of the two axes, by a 90° rotation of that polarization axis, for example, using a rotating or chiral material or by a succession of two quarter-wave plates, and 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 creating fringes whose positions depend on said phase difference. Optical amplifier

[0180] An "optical amplifier" is a device that allows the duplication of a photon introduced into it, in particular, the second photon of a pair of entangled photons, while preserving its polarization state.

[0181] Preferably, the optical amplifier is a fiber-doped amplifier.

[0182] For example, an erbium amplifier (EDFA), for example 4 m long, can be used, in which the photon to be amplified is introduced at the same time as an amplifying wave of shorter wavelength, which allows the wave corresponding to the introduced photon to be amplified, with gains that can be on the order of 37db / m.

[0183] One can also use a doped fiber amplifier (DFA) using a dopant other than erbium.

[0184] Alternatively, the optical amplifier is, for example, a vertical cavity amplifier (VCSOA), or a semiconductor-type amplifier (SOA). Anti-reflective coatings

[0185] To avoid the loss of photons, antireflective layers are preferably used at the interfaces between adjacent transparent media of different refractive indices through which photons pass, as well as at the interfaces of prisms and birefringent plates through which photons pass, the antireflective layer being preferably adapted to the refractive index or indices of the material and to the angle or angles of incidence and the directions of polarization as well as to the wavelength of the photon which must pass through it. Dichroic filters

[0186] The first and / or second receiver preferably includes one or more dichroic filters allowing only photons of a given wavelength to pass through, in particular a prism made of a dispersive transparent material, the filter(s) preferably being placed in front of the measuring instrument(s), or in front of the optical selector for the first receiver, especially if the refractive indices of nonlinear materials are modified by the application of powerful light fluxes. Photon allocation to information with synchronized clocks

[0187] When the photons arrive at the second receiver, it is useful to be able to differentiate whether they should be assigned to the transmitted information, whether it is information transmitted several times, or whether it is information that would not have been encoded on a pair of entangled photons.

[0188] Indeed, photon emissions are sometimes irregular, and an SPDS type emitter such as mentioned above may, for example, emit a double pair of photons unintentionally.

[0189] The transmitter and each of the receivers preferably include a clock, with the clocks of the transmitter and the receivers being synchronized with each other.

[0190] This allows, when combined with knowledge of the time of flight of photons between the emitter 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.

[0191] 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 δt' before the next reception period.

[0192] The second receiver preferably records the bits received for each reception period. It then advantageously transmits to the first receiver from time to time, especially if the device uses reflection to transmit a bit or a trit, for example every 3000 reception intervals, or every 100 photon-free reception intervals, a list of reception periods for which it did not receive 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 reflected photons during these same periods, especially if the device does not have a photon detector.

[0193] The transmission of this list can be done by instantaneous communication using the method according to the invention described below, or by a conventional means of communication. Upon receiving this list, the first receiver then transmits the bits corresponding to those transmission periods, for which no photon reached the second receiver.

[0194] Alternatively, the first receiver uses only two different measuring instruments to transmit information, one detecting linear polarizations, the other circular polarizations.

[0195] The first receiver then retransmits each bit while selecting the appropriate measuring instrument for 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, allowing it to select the measuring instrument to use for the transmission of the next bit.

[0196] The second receiver, upon receiving photons during the transmission periods, and if it receives any, measures for each transmission period their polarization state and deduces the bit that it must add to the list of received bits.

[0197] If the transmission line between the transmitter and the first receiver has a certain opacity and can absorb a certain proportion of the photons that pass through it, some photons may arrive at the second receiver during the reception periods with random polarizations.

[0198] The second receiver can then be configured to recognize at least some of the photons arriving in a polarization state that cannot be that of an entangled photon absorbed or reflected at the first receiver. Clock discrepancy

[0199] Preferably, the clocks of the system components, namely the transmitter and the two receivers, are configured to take into account the phenomenon of different time flow in different locations, including the different altitudes of each of the components. Synchronization of transmission periods between receivers

[0200] A process can be implemented to allow the first and second receivers to synchronize their clocks.

[0201] For example, when measuring a first photon, the first receiver records, using its own clock, the time at which said photon struck the measuring instrument.

[0202] The recorded time is then transmitted to the second receiver along with, preferably, the transmission interval references, including the time of and optionally the duration during which the photon was expected.

[0203] The second receiver records the time of reception 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 when the first photon hit 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.

[0204] If the transmission lines between the transmitter and either 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, then one of the receivers can communicate this average time to the other receiver.

[0205] The average time can be calculated by determining the average reception time of each photon, or only of the first and last photons received. The predetermined number of photons sent, or the duration of their transmission, is preferably adjusted based on factors such as the transmission / loss ratio of photons on each of the two paths between the transmitter and the receivers, and the average frequency of photon transmission.

[0206] Since the transit times of photons between the transmitter and each receiver vary, the clock synchronization between each receiver can differ depending on whether information is being transmitted in one direction or the other. Each receiver can therefore have a synchronization register used to increment or subtract a time interval from its clock, adjusted during synchronization, to determine the time of a synchronized clock for receiving information from the other receiver. Transmission between transmitter and receiver

[0207] A process can be implemented to synchronize the periods of sending photons to the receivers and the periods of reception at the receivers, these periods being time intervals during which photons can leave the emitter or reach the receiver.

[0208] To this end, the transmitter may 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 the sending of the signal.

[0209] Upon receiving the 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 time of the start of the photon transmission period during which the signal was sent, or if it was sent outside of a transmission period, the start of the previous transmission period, and does the same with the signal reception time and the time of the start of the reception period.

[0210] If the difference between the date of signal transmission 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 the opposite in the case of the difference.

[0211] The calibration is advantageously repeated several times and the results are averaged, allowing the clocks to be adjusted with a precision greater than the imprecision of the sending and receiving times of said light signals.

[0212] 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. Photon allocation to information without a synchronized clock

[0213] As an alternative to synchronized clocks, the first receiver may include 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 an element arranged to absorb the first photon in a predetermined polarization different from the polarizations of the detector-transmitters.

[0214] The polarizations of the detector-transmitters are preferably complementary, so that any photon directed towards an absorbing waiting element is absorbed.

[0215] Detector-transmitters are preferably arranged to detect the polarization of photons in at least four different polarizations, these polarizations being grouped in complementary pairs such that any photon directed towards a detector-transmitter is thus detected and absorbed regardless of its initial polarization.

[0216] The detector-transmitter(s) of the first receiver are used to send information by selecting the pair of detectors used.

[0217] Each photon received by the first receiver during a predetermined period, also referred to as the "rest period", after the receipt 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 receivers' clock, and the start of this rest period being determined by the sensor or one of the two sensors absorbing the photon that was used to send the information.

[0218] The second receptor 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 is subtracted the imprecision of the clock of the receivers, 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.

[0219] 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 towards the waiting element are received in a time less than the rest period less the imprecision of the clock of the receivers.

[0220] This process has the advantage of not requiring a switch at the emitter to restrict entangled photon emissions, nor clock synchronization.

[0221] The detector-transmitter(s) of the first receivers can also serve simultaneously as a waiting element, especially if the polarization in which they detect photons is adjustable and can therefore be adjusted to the polarization used by the waiting element to absorb photons. Noise reduction device

[0222] Optical amplifiers tend to emit photons in the opposite direction to the propagation signal, either during signal amplification or in the absence of a signal, after molecules or atoms of the amplifying medium have been excited by a pump signal.

[0223] The second receiver includes, for example, a switch positioned in front of the optical amplifier, in order to limit the number of photons emitted by the amplifier towards the entangled photon source of the device.

[0224] 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 within a predetermined time interval.

[0225] The switch of the second receiver can be connected to the measuring instrument of the second receiver, so as to prevent light from passing in either direction from the arrival of a first photon until the next photon is expected or a predetermined time before that moment, for example half of the rest period defined above.

[0226] Alternatively, the switch of the second receiver can allow photons to pass only during the periods when they are expected, in particular during the aforementioned photon processing time intervals. Assignment of photons to information without a synchronized clock using low-transparency optical transmission methods

[0227] Optical fibers, although transparent, do not transmit all the photons presented at their input. A loss of 0.20 dB per kilometer is common, resulting, for example, in a 10 dB loss over 50 km, or 90% of the photons.

[0228] The effect of photons lost in transit between the emitter and the first receiver is, however, different from the effect of the loss of photons lost during their transit to the second receiver; the entangled photons of the photons lost between the emitter 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 potentially information-carrying photon, that is to say, one whose entangled photon reached the first receiver.

[0229] Furthermore, the polarizations of photons arriving at the second receptor after their entangled photons have been absorbed in transit to the first receptor are not necessarily equally distributed among all possible observable polarizations.

[0230] Therefore, for information transmission, we preferentially use pairs of complementary polarizations for which corresponding polarizations observed at the second receptor are the fewest when the entangled photon of the photon detected at the second receptor has been absorbed during its transit to the first receptor.

[0231] The invention further relates to a calibration method for a system as defined above, enabling the determination of two Jones matrices, one of which allows the calculation of the polarization of a photon arriving at the second receiver as a function of the polarization of a photon absorbed at the first receiver, in which, preferably, the number of different polarizations observable at the second receiver is greater than twice the inverse of the photon transmission ratio between the emitter and the first receiver, the method consisting of: configure the complex absorber of the first receiver to absorb the photons received at the first receiver in one of two complementary polarizations of an absorption polarization pair, successively generate 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 polarization state, count for each polarization in which a photon is received at the second receiver the number of photons that have reached said second receiver with that same polarization, stop sending the 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,Given that these polarizations are considered to correspond to the absorption polarizations of photons at the first receptor, calculate the two possible Jones transformation matrices of the polarizations that allow us to deduce the polarization of a photon received at the second receptor from the polarization of a photon received at the first receptor.

[0232] 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 by their respective reception times, also makes it possible to select, among the two calculated Jones matrices, the one which allows the polarization of the photons received at the second receiver to be calculated as a function of the polarization of their entangled photons possibly received at the first receiver.

[0233] The following method can also be used to transmit information from the first to the second receiver, a method comprising the steps of: to successively generate 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 relative to their polarization state, for each piece of information to be transmitted, configure the complex absorber of the first receiver to absorb an NPT number of transmission photons in a predetermined complementary polarization pair called the "absorption polarization pair" corresponding to the information to be transmitted, then, if the next piece of information to be transmitted is not already known or is identical to the information just transmitted, configure the absorber in a polarization pair called the "waiting polarization pair" and, if said information is identical to the information just transmitted,Count at least NPT photons absorbed in this "standby polarization pair". At the second receiver, count, for each complementary polarization pair, the number of photons received in one of the two polarizations of said polarization pairs since the possible last reception of a signal. As soon as this counter exceeds a predetermined threshold number NSP for one of the pairs and the complementary polarization pair is different from that of the last received signal, consider the information corresponding to this polarization pair as a new signal, and if this last piece of information does not correspond to the standby polarization pair, add this information to the list of received information.

[0234] 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.

[0235] For example, to transmit information, we would use: transmission lines between the transmitter and each of the receivers exhibiting an attenuation of 10 dB, i.e. a loss of 90% of the photons, transmission lines between the complex absorbers, configured to absorb the photons in 450 pairs of complementary polarizations, these pairs representing 80% of the photons received at the second receiver during an absorption of their entangled photons in their transits to the first receiver, we can choose 200 photons for NPT and 6 for NSP, which allows us to obtain, according to the inventor's calculations, a transmission error rate which would then be less than 1 in 10,000.

[0236] 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 about 5°, the encoding of 1200 photons at the first receiver (therefore NPT=1200), the threshold number NSP being fixed at 14, makes it possible to obtain, according to the inventor's calculations, an error rate of less than 1 in 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. Photon pair processing sent simultaneously

[0237] The emitter can sometimes send pairs of entangled photons very close to each other. Therefore, the photon detectors at the first receiver preferably count the number of absorbed photons, and not just the number of photon impacts on that first receiver. This count can, for example, take into account the intensity of the electromagnetic wave incident on the photon detectors.

[0238] Groups of photons can thus arrive almost simultaneously at the second receiver, which is unable to distinguish 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 groups of photons arriving simultaneously at the second receiver—that is, whose generated light intensity is, for example, 50% greater than the intensity generated by a single photon—advantageously does not result in an increment of the counters for photons received in various polarizations. However, it is sometimes possible that a plurality of photons reach the first receiver, but only one of their entangled photons reaches the second receiver, in which case it is counted. Device performance

[0239] The use of lossless or low-loss lines between the transmitter and the first receiver, allowing photons to pass through a vacuum, for example, makes it possible to reduce or avoid photons received at the second receiver with random polarization.

[0240] Similarly, using precise measuring instruments at the second receiver that either increase the number of complementary polarization pairs or ignore a large number of photons with random polarizations can allow: to increase the transmission distance of photons, to increase the bit rate by decreasing the number of NPT transmission photons.

[0241] An increased switching speed of the polarization of the complex absorber of the first receiver allows for an increase in the sending frequency of the entangled photons sent by the emitter.

[0242] Increased temporal accuracy of the polarization detectors of the second receiver, which makes it possible to distinguish the interference of various photons received very close together in time, also allows the use of a larger flux of entangled photons, but also to reduce the number of receptions of photons received "simultaneously", as described above.

[0243] This process has the advantage of not requiring the installation of a switch at the emitter to restrict the emission of entangled photons, nor clock synchronization. Photon return processing to the transmitter

[0244] Photons are sometimes reflected back to the emitter from the receivers. To prevent them from being reflected back by the emitter to one of the receivers, the cavity or material in which the entangled photons are produced by wave mixing, whose refractive index is non-linear, is preferably surrounded or covered with a material that absorbs light having a wavelength equal to that of the entangled photons. Quantum communication processes

[0245] The invention also relates to a quantum communication method using the system defined above, comprising the steps of: generate a pair 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, the second receiver being located further from the emitter than the first receiver on the propagation path of the second photon, such that it arrives there later; modify, 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, excluding exactly two pairs of perpendicular linear polarizations where the polarization directions of one of the pairs are at 45° to the polarization directions of the other pair; absorb, by means of an absorption instrument,The first photon, in one of the two complementary polarizations of the selected pair, is transmitted to the second receiver. The second photon is then duplicated into a stream of multiplied photons using an amplification device. The light thus created retains the polarization state of the second photon. The average polarization state of the light stream is measured, and the polarization state of the first photon is determined from this measurement, in order to deduce the information transmitted by the first receiver.

[0246] The complementary photon pair is preferably selected from at least three different pairs of complementary polarizations.

[0247] The pair of complementary polarizations is, for example, selected from 210 distinct pairs of absorption polarizations, including polarizations spaced 9° apart in their polarization direction and 9° out of phase.

[0248] The invention also relates to a quantum communication method using the system defined above, comprising the steps of: to generate a pair 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, the second receiver being located on the propagation path of the second photon further from the emitter than the first receiver, such that it arrives there later, to select, according to 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, by means of 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,to trap said first photon in a protective device to prevent its absorption at least until the second photon reaches the second receiver; at the second receiver, to 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; to measure the average quantum state of the stream of multiplied photons and to determine, based on 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.

[0249] Preferably, the polarization of the entangled photon pair is indeterminate in the polarization(s) of the complementary polarization pair in which the instruments of the first receiver absorb them.

[0250] The pair of entangled photons reaches, for example, the receptors with a linear entangled polarization, one of the two complementary absorption polarizations being circular, the second receptor being arranged to distinguish whether the average polarization of the multiplied photon flux is circular or linear, and to determine according to this distinction whether the first photon has been measured or not.

[0251] Alternatively, the entangled photon pair reaches the receptors with a circularly entangled polarization, the quantum state of absorption of the photons being a linear polarization, the second receptor being arranged to distinguish whether the average polarization of the multiplied photon flux is circular or linear, and to determine according to this distinction whether the first photon has been measured or not.

[0252] Alternatively, the entangled photon pair reaches the receivers with a vertical or horizontal linear polarization, 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 multiplied photon flux (P20) is at 45 or -45°, or the vertical or the horizontal, and to determine according to this distinction whether the first photon has been measured or not. Information transmission

[0253] 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 binary type, in the form of bits, or discrete or continuous values.

[0254] Preferably, several pairs of entangled photons are generated successively by the emitter, each pair of photons enabling the transmission of information, for example of a binary type, from the first receiver to the second receiver.

[0255] For example, we can choose to absorb the first photon at the first receiver to transmit a bit 1 and reflect it to transmit a bit 0. Measuring the average quantum state of the multiplied photon flux at the second receiver then allows us to determine whether a bit 1 or a bit 0 is transmitted from the first receiver almost instantaneously.

[0256] Several methods can be implemented to secure communication and avoid transmission errors, due for example to double pairs of photons emitted simultaneously.

[0257] For example, during time intervals previously established using the clocks described above, only the first photon reaching a receiver is preferably considered, with subsequent photons being ignored.

[0258] As described above, photons can be counted as they arrive at a polarization detector. If the count reveals the arrival of more than one photon during a predefined time interval, the bit is not transmitted during that interval, and is instead transmitted, for example, in the next time interval or, preferably, the same bit is retransmitted.

[0259] At the second receiver, counting the photons arriving in the time interval where they are expected can advantageously allow the creation of a temporary list of unreceived bits. Two-way communication

[0260] To enable bidirectional communication, that is, to allow each of the two receivers to transmit information to the other receiver, a plurality of transmitters can be used.

[0261] The system according to the invention may in particular include a second emitter 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.

[0262] Alternatively, at least some of the photons can be made to travel an indirect path in order to lengthen their transport time to one of the receivers, for example by reflecting the photons on one or more intermediate mirrors, or by making them pass through media with high refractive indices, or by transporting them in optical fibers of varying lengths.

[0263] This extended path can, for example, alternate at a fixed or variable rate, depending on the needs, with the unextended path, so that entangled photons can sometimes be used to transmit information from one point to another, and sometimes in the opposite direction. Optical switches upstream of the receivers, synchronized with the switch attached to the transmitter, can send the photons along an extended path. These switches can then be installed to send said photons to receivers corresponding to the first type of receiver, as described above, or conversely, to the second type of receiver.

[0264] Method of transmitting a key and verifying that this transmission has not been intercepted.

[0265] We can verify that information transmitted by a stream of photons from the transmitter to the second receiver has not been received by implementing the following steps: the second receiver establishes a first list of the reception dates of the photons that carried the information as well as the relative polarization designating which 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 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 never reached the first receiver, two entangled photons having different relative polarizations;If the number of elements in the second restricted list of entangled photon pairs, where each of the two photons has reached its respective receptors, is less than the product of a predetermined ratio by counting the elements in the first restricted list of entangled photon pairs, where each of the two photons has reached its respective receptors, then the information is declared to have been transmitted but not intercepted.

[0266] The following steps can then be taken: if the information is declared to have been transmitted unlistened to, 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 good reception 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 when the first receiver receives 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.

[0267] A polarizing filter can be placed upstream of the second receiver. Method for comparing a first dataset and a second dataset

[0268] The invention also relates to a method, implemented by at least one device, for comparing a first dataset and a second dataset, in particular to determine whether these two datasets are identical, this method comprising the steps of: a) mix a number, called the mixer number, with the first dataset, using a mixing function, 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 dataset assumed to be the hash of the second dataset mixed with the same mixer number as that used in step a) and using the same mixing function.

[0269] Thanks to the invention, and in particular to the mixing of the first dataset with a mixer number before hashing, it becomes very unlikely that data similar to this first dataset will, after being mixed with the same mixer number, have the same hash as the first mixed dataset.

[0270] Preferably, the method according to the invention does not require the simultaneous presence of two sets of data in the device.

[0271] Preferably, the mixer number is generated randomly.

[0272] The mixer count is preferably generated by the device. Alternatively, the mixer count is generated by another trusted device.

[0273] The mixing number can be generated based on a pair of input values ​​that are physical quantities, at least one of which varies continuously, such as temperature and time, or on a quantum phenomenon. For example, such generation can be based on the two Young's slits that a photon chooses to use to pass through a plate.

[0274] Preferably, the mixing operation in step a) is carried out by the device. Alternatively, the mixing is carried out by another reliable device.

[0275] The shuffling function combines the first dataset and the shuffling number. It is preferably a logical XOR function that adds the bits of the first dataset to those of the shuffling number, one by one. Since the size of the shuffling number is usually smaller than the size of the first dataset, it is possible to add the bits of the shuffling number to the first or last bits of the first dataset using an XOR operation.

[0276] The mixer number can have the same size as the first dataset. In this case, the addition using the XOR function is performed on all bits, one by one.

[0277] Alternatively, the shuffle function is a suffix function consisting of adding the shuffler number to the end of the first dataset.

[0278] The shuffler function can even be an encryption function using the shuffler number as the encryption key to encrypt the first set of data.

[0279] In one embodiment, the mixing function is a combination of an XOR function, a suffix function consisting of adding the mixer number to the end of the first dataset, and an encryption function using the mixer number as the encryption key to encrypt the first dataset.

[0280] Preferably, the data from step b) is hashed by the device. Alternatively, the hashing is performed by another trusted device.

[0281] Preferably, the hash function is chosen from SHA1, SHA2, SHA256 and MD5 and the Jenkins function. First integrity verification process from a message

[0282] A first variant of the method according to the invention is a method for verifying, by means of the device, the integrity of a message from a sender, the method comprising the steps of: i. receive, by means of the device, the message and a message identifier, said message forming the first data set, ii. generate the mixer number, iii. carry out steps a) and b), in which the message is mixed with the mixer number and then hashed, iv. optionally encrypt the mixer number, v. send, by means of the device, the message identifier and the optionally encrypted mixer number to the message sender, vi. receive, by means of the device, the third encrypted data set, preferably with the message identifier, from the sender, vii. decrypt the third data set, and viii. carry out 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.

[0283] By "integrity" of the message, we mean its non-alteration, for example by a malicious third party who would have intercepted it during its transmission.

[0284] The message identifier can be a sequence of alphanumeric characters and / or symbols that can be converted into a numeric word by means of, among other things, an ASCII code.

[0285] The message identifier may contain the sender's identifier and a message sequence number.

[0286] The sender's authentication is ensured in particular by the decryption operation carried out in step vii.

[0287] Decryption can be performed using an encryption key kept secret between the device and the sender.

[0288] Preferably, the mixer number is kept secret and a renewable key of the size of the hash (third set of data) is used, notably with an XOR as the encryption function.

[0289] Another solution is to keep the mixer number secret and use a non-renewed symmetric key with a symmetric encryption function.

[0290] Alternatively, the mixer number is kept secret and a non-renewed asymmetric key pair is used with an asymmetric encryption function.

[0291] Alternatively, the mixer number is kept secret and a non-renewed symmetric key is used with a symmetric encryption function.

[0292] Alternatively, the mixer number is a renewable key and another renewable key of the size of the hash (third dataset) is used, notably with an XOR as the encryption function.

[0293] Alternatively, the mixer number is a renewable key and a non-renewable key of the size of the hash (third dataset) is used, notably with an XOR as the encryption function.

[0294] Alternatively, the mixer number is a renewable key and a non-renewed symmetric key is used with a symmetric encryption function.

[0295] Alternatively, the mixer number is a renewable key and a non-renewed asymmetric key is used with an asymmetric encryption function.

[0296] 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.

[0297] In another embodiment, the mixer number is randomly generated after each use. This mixer number can be encrypted with a one-time key. The mixer number can also be encrypted using a symmetric or asymmetric function.

[0298] This first variant of the invention makes it possible to ensure both the integrity of the received message and the identity of the sender of the message.

[0299] The steps relating to sending and receiving data can be carried out using the same communication protocol or different communication protocols. For example, data received in step i is received via Wi-Fi, data sent in step v is sent via 4G, and data received in step vi is received via WiMAX.

[0300] In step i, the device can also receive a sender identifier. This identifier is useful if the device is likely to receive messages from various senders, as such an identifier allows it to choose the encryption keys to use to encrypt or decrypt the information exchanged with the sender during the encryption and decryption operations described in this first embodiment of the invention.

[0301] Preferably, the process according to this first variant includes, 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 mixer number, identify, using the message identifier, the message sent to the device, mix the message with the optionally decrypted mixer number using the mix 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 identifier.

[0302] The optional encryption of the mixer number in step iv is preferably performed by the device.

[0303] Optional encryption of the mixer number helps prevent this number from being intercepted and modified by a malicious third party.

[0304] Preferably, the optional encryption of the mixer number is performed using a one-time key at least as long as the number itself. Since the key is one-time use only, a new key is used each time a mixer number is sent.

[0305] 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.

[0306] Alternatively, the optional encryption of the mixer number is asymmetric, and is performed either using a sender's public key known to the device, so as to allow decryption by the sender using their associated private key, or using a device's private key whose public key is known to the sender.

[0307] This prevents a third party from knowing or changing the mixing number.

[0308] Preferably, the decryption of step vii is performed by the device.

[0309] Decryption of step vii can be performed using a symmetric key, if encryption of step iv is performed using a one-time-use key.

[0310] Alternatively, decryption of step vii is performed using a one-time key if encryption of step iv is performed using a symmetric key.

[0311] 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 which was used to encrypt the hash received in step vi. The device is thus able to certify the identity of the sender.

[0312] The mixer number can 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.

[0313] Preferably, private, symmetric, and one-time-use encryption keys and mixer numbers are undetectable and unobservable by third-party devices, in order to prevent eavesdropping on data sent by the sender or device from generating and transmitting second sets of fraudulent data that would falsely recognize the integrity of messages received by the device but transmitted by a sender other than the one legitimately supposed to hold said keys.

[0314] If the encryption key X of the shuffler x is known, then the hash of the shuffled message can be known, since it suffices to decrypt the encryption of x and calculate the message shuffle before hashing it. We can then also guess the key Y encrypting the hash or know that it belongs to a small universe, since both the hash of the shuffled message and its encryption with Y are 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 that depends on the encryption key X. Observing a plurality of transmissions reveals a plurality of functions F, and the values ​​of the keys X and Y lie at the intersection of these functions. It is preferable to avoid this situation.It is therefore recommended either to use values ​​for the key X or the key Y 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 large the universe resulting from the intersection of these universes deducible at each observation. It is not recommended to take the randomly generated mixer number x for the key Y. More precisely, if the mixer number x is used as the encryption key Y, or if the key Y is calculated as a function of the mixer number x using a defined formula, knowing the encrypted value C of the mixer number x encrypted with the key X, the mixer number x, and therefore Y, becomes another function G of the key X; and the keys X and Y would then be found at the intersection of the function F and this new function G.Preferably, key X or key Y should be renewed after each exchange.

[0315] The device may also 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 mixer number or the encryption key used to encrypt the hash.

[0316] Alternatively, the device can impose a predetermined number of successive unsuccessful attempts to decrypt messages arriving from or sent by the same sender. After this predetermined number of attempts, and after a specified period, the device queues the received messages or the message sent by the same sender, or preferably ignores them, before attempting again to either decrypt the messages queued or resume decrypting the messages that continue to arrive after the specified period has expired. This approach is advantageously implemented by a device that sends a reply message to the sender of queued or ignored messages, informing them of the processing of their message.For example, three consecutive messages received from an unverified sender 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. Second integrity verification process from a message

[0317] A second variant of the method according to the invention is a method for verifying, by means of the device, the integrity of a message from a sender, the method comprising the steps 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. carry out steps a) to c), the integrity of the message being ensured if the hash obtained in step b) and the third data set decrypted in step ii) are identical.

[0318] Decryption can be performed using an encryption key kept secret between the device and the sender.

[0319] Preferably, the mixer number is kept secret and a renewable key of the size of the hash (third dataset) is used, notably with an XOR as the encryption function.

[0320] Alternatively, the mixer number is kept secret and a non-renewed symmetric key is used with a symmetric encryption function.

[0321] Alternatively, the mixer number is kept secret and a non-renewed asymmetric key pair is used with an asymmetric encryption function.

[0322] Alternatively, the mixer number is kept secret and a non-renewed symmetric key is used with a symmetric encryption function.

[0323] Alternatively, the mixer number is a renewable key and another renewable key of the size of the hash (third dataset) is used, notably with an XOR as the encryption function.

[0324] Alternatively, the mixer number is a renewable key and a non-renewable key of the size of the hash (third dataset) is used, notably with an XOR as the encryption function.

[0325] Alternatively, the mixer number is a renewable key and a non-renewed symmetric key is used with a symmetric encryption function.

[0326] Alternatively, the mixer number is a renewable key and a non-renewed asymmetric key is used with an asymmetric encryption function.

[0327] 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.

[0328] In another embodiment, the mixing number is randomly generated after each use. This mixing number can be encrypted with a one-time key. Alternatively, the mixing number is encrypted with a symmetric or asymmetric function. Preferably, the method according to this second variant of the invention comprises, before step i, the steps of: generate, by the sender, the mixer number, mix the mixer number with the message, using the mix 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 to the device the message, the third encrypted data set and the encrypted mixer number.

[0329] These steps are carried out by the authentic sender and allow for the detection of message alteration by an unauthorized third party.

[0330] The decryption in step ii of the mixer number and the third dataset is preferably performed by the device.

[0331] Preferably, the encryption of the mixer number is performed using a one-time key, and the encryption of the third dataset is performed using a symmetric key, the symmetric key preferably being renewed occasionally.

[0332] Alternatively, the encryption of the mixer number is performed using a symmetric key, and the encryption of the third dataset is performed using a one-time-use key, with the symmetric key preferably being renewed occasionally.

[0333] The encryption of the mixer number and the encryption of the third dataset can also be of the same type, or of different types, these types of encryption being able to use symmetric keys or asymmetric keys.

[0334] If an asymmetric key pair is used for encrypting the mixer number, the private key of this pair is preferably kept by the device, with the corresponding public key then being known to the sender.

[0335] The encryption of the third set of data can be performed using a private key held by the sender, the corresponding public key then being known to the device.

[0336] Thus, by decrypting the mixer number and the third set of data, the device is able to certify the sender's identity.

[0337] The encryption of the mixer number and that of the third dataset can be performed using the same encryption function, particularly when the encryption of the mixer number is asymmetric.

[0338] Alternatively, the encryption of the mixer number and that of the third dataset are performed by two different encryption functions.

[0339] Preferably, the types of encryption functions to be used are part of the sender and device configuration, before communication is established between the two. Third integrity verification process from a message

[0340] A third variant of the method according to the invention is a method in which the first dataset is present in the device and the second dataset is present in a second device, the method comprising the steps of: i. implement steps a) and b), ii. encrypt the mixer number, iii. send, by means of the device, the encrypted mixer number to the second device, iv. receive, by means of the device, an encrypted hash of the second dataset, v. decrypt the encrypted hash, and vi. implement step c).

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

[0342] Preferably, the mixer number is kept secret and a renewable key of the size of the hash is used, notably with an XOR as the encryption function.

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

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

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

[0346] Alternatively, the mixer number is a renewable key and another renewable key of the size of the hash is used, notably with an XOR as the encryption function.

[0347] Alternatively, the mixer number is a renewable key and a non-renewable key of the hash size is used, notably with an XOR as the encryption function.

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

[0349] Alternatively, the mixer 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 embodiment, the mixer number is randomly generated after each use. This mixer number can be encrypted with a one-time key. The mixer number can also be encrypted using a symmetric or asymmetric function.

[0352] Preferably, the process according to this third variant of the invention comprises, between steps iii and iv, the steps of: receive, by means of the second device, the encrypted mixer number, decrypt the mixer number, create a modified copy of the second dataset using the mixer number and the mixer function, hash the modified copy of the second dataset using the hash function, encrypt the hash resulting 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 dataset.

[0353] The encryption of the mixer number in step ii and the decryption of the encrypted hash in step v are preferably performed by the device.

[0354] Preferably, the encryption of the mixer number is performed using a symmetric encryption key shared with the second device.

[0355] Hash encryption can be performed using a one-time-use key, and mixer number encryption can be performed using a symmetric key that is renewed occasionally.

[0356] Alternatively, the mixer number encryption is performed using a one-time-use key and the hash encryption is performed using a symmetric key that is renewed occasionally.

[0357] Mixer number encryption and hash encryption can also be of the same type, or of different types, these types of encryption being able to use symmetric keys, including one-time use keys, or asymmetric keys. Method for generating shared quantum keys

[0358] The invention can be used in quantum communication processes, notably in E91 Quantum Key Distribution, where a pair of entangled photons is used to generate a secret shared between two photon receivers.

[0359] Another aspect of the invention relates to a method for generating a shared quantum key using a quantum communication system, the system comprising: an entangled photon emitter, 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 disposed on the first propagation path, comprising a first polarization measurement basis configured to measure a polarization state of a photon received by the first receiver; and a second receiver disposed on the second propagation path, comprising a second polarization measurement basis configured to measure 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; wherein the first receiver establishes a first list containing the dates of receipt and a second list containing these dates of receipt and the polarization states of the photons received by the first receiver, and the second receiver establishes a third list containing the dates of receipt and a fourth list containing these dates of receipt and the complementary polarization states of the photons received by the second receiver; wherein the first list and / or the third list are exchanged between the first receiver and the second receiver and are preferably electronically signed;in which, upon receiving the third and / or first list, respectively, the first receiver and / or second receiver establishes a fifth list containing 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;in which, 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 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;wherein the respective signatures of the sixth and seventh lists are exchanged between the first and second receivers, according to the method of the invention, preferably with a mixer number renewed each time and a renewed one-time key used for hash encryption; wherein said sixth and seventh lists can be used as a shared list of random bits. From this shared list, one can, for example, extract one-time keys or lists of random rotation angles of polarization measurement bases.

[0360] A signed message can be exchanged between the two receivers before using the sixth and seventh lists as one-time keys.

[0361] The polarization measurement bases can be made to rotate randomly and simultaneously by the same angle, which is kept secret, between the two receivers.

[0362] The sixth and seventh lists can be used as lists of random rotation angles of the polarization measurement bases.

[0363] Photons are preferably sent in a fixed polarization which is not the polarization of photons that can be measured by the receivers, 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° to the direction of linear polarization in which the polarizations of the photons are detected by the receivers.

[0364] The direction of the polarization angle at which the polarizations are detected by the receivers can be periodically and randomly changed by the same angle on both receivers, preferably by 0° or 45°, and preferably with the linear polarization angle at the emitter being changed by the same angle if the emitter is indeed emitting linearly polarized photons. The change can, for example, occur every millisecond. This prevents an eavesdropping device from sending pairs of photons to both receivers in known polarizations that can be detected by the receivers, with one photon having the complementary polarization of the other and arriving at the receivers simultaneously according to "synchronized" clocks, because the direction in which the photons can be detected by the receivers may not be known to the eavesdropping device.

[0365] The polarization angle can be modified, for example, by means of a bypass circuit for photons upstream of the receivers. A first switch can deflect the incident photon towards a photon polarization rotation device, and a second switch allows the photon exiting said polarization rotation device to be sent to said receiver. Thus, in one 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 ηm (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 separating the light into two linearly polarized beams of light which each pass through two quarter-wave plates forming an angle between them, such that the light leaves the second linearly polarized quarter-wave plate at a certain angle to the polarization direction at which it reaches the first quarter-wave plate, the two linearly polarized beams of light leaving the second quarter-wave plates being joined into a single beam by passing through a second birefringent prism.

[0366] Angle changes can be fixed according to one-time-use 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 photons in a circularly polarized state while the readers read the photons in a linearly polarized state—the one-time-use key can be renewed using keys generated by the shared Quantum Key generation process described here.

[0367] By "complementary polarization state of a given photon", we mean the polarization state in which the entangled photon of said given photon should be found.

[0368] Furthermore, the photon path is preferably physically protected against the insertion of a spying device in a first zone, in the part where the photons propagate without becoming entangled. For example, if the photon path is longer by a measured length 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 that measured length.

[0369] For example, this length can be physically measured, particularly if the photons propagate through optical fibers. Similarly, and especially during free-space propagation, the measurement can be performed by placing truly synchronized clocks on the two receivers (as opposed to the synchronized clocks described above), and by verifying at the time of the measurement that no eavesdropping device has been inserted between the transmitter and the receivers.

[0370] Here again, the photon path is preferably physically protected in a second zone located upstream of the first zone, if one exists, or upstream of the detector, if the first zone does not exist, against the insertion of a spying 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.

[0371] 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 and second zones, thus arriving at a different time than it would have arrived if no spy device had interfered, and this time difference will be perceptible to the second receiver.

[0372] A spy transmitter can send a first photon entangled with a second photon to the first legitimate receiver 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 must send a photon polarized in the appropriate state, but this photon must first propagate to the second protected area and then traverse the protected area, which takes more time and, consequently, will arrive at a different time than when the initial spy photon was detected by the first receiver.

[0373] On the other hand, if a spy device sends a first photon entangled with a second photon to the second receiver and detects its polarization state, it could then send a photon with the same polarization to the first receiver; 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.

[0374] 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, assuming nothing interfered with the transmission process of the entangled photons. For example, if the entangled photons are read in corresponding states on both receivers in 99.9% of cases—that is, if the reading of their polarization state is correct in 99.9% of cases—the sixth and seventh lists can be 500 bits long, and the first and second lists can have 5000 successive reception times. This is assuming 90% of the entangled photons are lost between the photon emitter and the receivers, with each photon receiver, regardless of which receiver it is, having only a 10% chance that its entangled photon was received by the other receiver. Fourth method for verifying the integrity of a message

[0375] A fourth variant of the method according to the invention is a method for verifying that a dataset present in the device has not been modified between two times d1 and d2, this dataset constituting, at time d1, the first dataset and, at time d2, the second dataset, the method comprising the steps 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 mixer function, iv. hash the modified copy using the hash function to form the third dataset, and v. implement step c).

[0376] Advantageously, the process according to this fourth variant does not require storing the dataset securely. Computer program product

[0377] The invention also relates to a computer program product containing instructions readable by a processor of a device to implement the process according to the invention, according to any one of the variants defined above. Brief description of the drawings

[0378] The invention will be better understood upon reading the detailed description that follows, the non-limiting examples of its implementation, and upon examination of the accompanying drawings, in which: [ Fig 1A ] represents in a partial and schematic way a quantum communication system according to the invention, [ Fig 1B ] represents in a partial and schematic way another quantum communication system according to the invention, [ Fig 2A ] partially and schematically represents a linearly polarized photon, [ Fig 2B ] represents in a partial and schematic way a circularly polarized photon, [ Fig 3 ] there figure 3schematically represents details of photon transmission from the emitter to the receivers, [ Fig 4A ] represents in a partial and schematic way an example of an optical selector according to the invention, [ Fig 4B ] represents, in a partial and schematic way, a variant of the selector of the figure 4A , [ Fig 4C ] represents in a partial and schematic way another example of an optical selector according to the invention, [ Fig 5A ] ] Fig 5B ] there Figure 5A and the figure 5B schematically represent an example of a polarization direction modifier comprising quarter-wave plates, [ Fig 5C ] there figure 5C schematically represents another example of a polarization direction modifier involving a chiral material, [ Fig 6 ] there figure 6 schematically represents an example of a polarization phase modifier, [ Fig 7] represents in a partial and schematic way an example of an instrument for absorbing a linearly polarized photon, [ Fig 8 ] represents in a partial and schematic way another example of an instrument for absorbing a linearly polarized photon, [ Fig 9 ] represents in a partial and schematic way an example of a second photon receiver comprising a doped fiber amplifier, [ Fig 10A ] represents in a partial and schematic way an example of a measuring instrument for the second receiver comprising a succession of semi-reflective plates, [ Fig 10B ] represents in a partial and schematic way an example of a Young interferometer used for the second receiver measurement instrument, [ Fig 11A ] is a functional diagram partially illustrating an example of how a quantum communication system works to transmit a bit 0, [ Fig 11B] is a functional diagram partially illustrating an example of how a quantum communication system works to transmit a bit 1, [ Fig 12 ] is a functional diagram partially illustrating an example of how a quantum communication system works to transmit a series of discrete values, [ Fig 13 ] is a functional diagram partially illustrating an example of a time-stamping process for the arrival of a photon in a receiver, [ Fig 14 ] partially and schematically illustrates the possibility of placing a "noise-canceling" device in front of the amplifier, [ Fig 15 ] represents in a partial and schematic way the possibility of using the system according to the invention to establish bidirectional communication between two locations, [ Fig 16 ] there figure 16 illustrates a variant of the implementation of a quantum communication system according to the invention, [ Figure 17 ] there figure 17 schematically illustrates a physical protection of the quantum communication system according to the invention, [ Fig 18 ] there figure 18 schematically illustrates optical protection of entangled photons in the quantum communication system according to the invention, [ Fig 19 ] there figure 19 schematically illustrates an example of a process for calculating a hash of a set of data. Description détaillée

[0379] We illustrated at the figure 1A a quantum communication system 1 according to the invention. The system comprises a transmitter 2 emitting a pair of entangled photons (P1, P2), the first photon P1 propagating along a propagation path D1 and the second photon D2 propagating along a propagation path D2 different from path D1. The photons P1 and P2 are emitted simultaneously.

[0380] 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 refer to the product emitted by the emitter 2.

[0381] The terms "measuring instrument" and "absorption instrument" are used interchangeably to refer to an instrument that absorbs a photon according to a certain polarization.

[0382] System 1 includes a first receiver 3, located on the propagation path D1 of the first photon P1, and a second receiver 4, located on the propagation path D2 of the second photon P2.

[0383] Receiver 3 is closer to emitter 2 than receiver 4, so that photon P1 reaches it before photon P2 reaches receiver 4. Photon P2 reaches receiver 4 for example after an additional travel time t tra corresponding to an additional travel path Ltra.

[0384] In the example considered, the receiver 3 comprises a complex absorber 31 including a polarization modifier 32 and an absorption instrument 35.

[0385] The complex absorber 31 is configured to absorb the photon in a polarization state selected from several different complementary polarization pairs, preferably at least three pairs.

[0386] The polarization modifier 31 is configured to transmit the photon P1 according to the selected pair of complementary polarizations, and the absorption instrument 35 determines which of the two states of the pair the photon P1 is in. Before entering the absorption instrument 35, the polarization state of the photon P1 is a superposition of the two states of the selected pair, weighted by certain probabilities, for example, in an equiprobable manner.

[0387] We illustrated at the figure 1B 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 P1, and an optical selector 30 disposed upstream of the measuring instruments 35 and configured to send the first photon P1 either to a birefringent prism 36 which guides the photon, according to the linear direction of its polarization, on paths D1' or D1" and then to one or the 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 D1.

[0388] The direction D3 is specifically chosen so that the photon P1 is not absorbed before its entangled photon is multiplied at the second receiver 4.

[0389] The system 1 preferably includes, as illustrated, a device 5 for protecting the quantum state of a photon located near the receiver 3, in particular on the propagation path D3 in the example considered.

[0390] This device allows, for example, to "trap" the photon P1 in the case where it is reflected by the optical selector 30 on the path D3, in order for example to prevent it from being measured or absorbed at least until the second photon P2 has reached the second receiver 4. A photon detector 5D (not shown) can be placed at the end of the device 5 to detect the photons which have been captured there, after their entangled photons have reached the second receiver.

[0391] The second receiver 4 includes 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 to be measured.

[0392] The transmission of photons P1 and P2 can occur in various ways and in various media. Photons propagate, for example, in an optical fiber or a waveguide, or even freely in space, whether the space is empty or filled with gas.

[0393] Photons can pass through several media with different refractive indices. For example, anti-reflective plates can be inserted between two media they pass through, if necessary, to avoid unwanted optical phenomena, particularly Fresnel reflection of the waves emitted by emitter 2.

[0394] The emitter 2 includes, for example, one or more selected lenses of sufficient size to ensure that the photons reach their respective receiver with low diffraction, for example allowing at least 99.99% of the emitted wave to reach the receiver.

[0395] The emitter 2 may also include a system, in particular an electronic device, for adjusting the initial directions in which the photons P1 and P2 are emitted respectively.

[0396] This adjustment can, for example, take into account the different refractive indices of the media traversed, and the modification of the trajectory of photons that can result, for example for a photon emitted from space that enters the atmosphere.

[0397] The wavelength of the emitted wave is selected, for example, according to the medium or media to be traversed; for example, photons in the infrared range are preferred when they have to pass through the atmosphere or air.

[0398] Transmitter 2, for example, generates entangled photon pairs using the spontaneous parametric frequency lowering (SPDC) process. Transmitter 2 is configured, for example, 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.

[0399] When emitted, photons P are, for example, linearly polarized, meaning that the corresponding electromagnetic wave has an electric field whose direction is perpendicular to its direction of propagation D. Where applicable, the polarization of the photons can be vertical V or horizontal H, as illustrated in the figure 2A .

[0400] The quantum state corresponding to the polarization of photons is sometimes indeterminate 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°.

[0401] In the variant illustrated at the figure 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 magnitude remains constant.

[0402] Where applicable, the polarization of photons is defined by the direction of rotation of the electric field, either clockwise C1 or counterclockwise C2. Before being measured, linearly polarized photons are in an indeterminate quantum state, considered as the superposition of two circular polarization states with opposite directions of rotation.

[0403] In some cases, two quarter-wave plates 6 and 8 can be introduced into the photon propagation paths between the emitter 2 and the receivers 3 and / or 4, as illustrated in the figure 3 .

[0404] 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 with respect to the wave having an electric field parallel to said ordinary axis.

[0405] The photons emerging from the blade 6 are for example transmitted by an optical fiber 7 to another quarter-wave blade which converts the circularly polarized fields into linearly polarized fields, before propagating to the receivers 3 or 4.

[0406] This conversion of the polarization of the emitted photons makes it possible, in particular, not to have to take into account at the receiver level the direction of the polarization of the photons emitted by the emitter.

[0407] The optical selector 30 can be made in various ways, some examples of which are illustrated in figures 4A to 4D.

[0408] The optical selector 30, for example, includes a liquid crystal controlled mirror as illustrated in the figure 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, thus controlling their refractive index. n C .

[0409] According to the refractive index n C , The incident photon P1 can be reflected on a propagation path D3, or it can pass through the blade 370 and be transmitted on a propagation path D1', which can be identical or different from the path D1, to the measuring instrument 35.

[0410] In an illustrated variant at the figure 4B , the photon P1 passes through the liquid crystal plate 370 and emerges along D3 or D1', the directions D1, D1' and D3 being, in the example considered, parallel.

[0411] 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.

[0412] Anti-reflective plates can advantageously be placed on each face of the 370 plate and adjusted according to the entry and exit angles of the photon when it passes through it.

[0413] In the variant illustrated at the figure 4C The optical selector 30 is a mirror controlled by nonlinear fibers. It comprises two optical fibers 330 and 335. Fiber 335, for example, is made of a nonlinear material.

[0414] The first photon P1, upon its arrival at the first receiver, enters the fiber 330. We can choose to simultaneously illuminate the fiber 335 with a light signal F, also called "control signal".

[0415] The signal F is a high-intensity light wave, for example emitted by a laser, and with a wavelength different from that of the photon P1.

[0416] If the fiber 335 is illuminated by the signal F, the photon P1 remains in the fiber 330 before, for example, passing through a prism 345 at the fiber output, which is located 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.

[0417] If fiber 335 is not illuminated by signal F, photon P1 is transmitted from fiber 330 to fiber 335. Photon P1 exits fiber 335 and passes, for example, through a prism 340 before being transmitted, for example, to the measuring instrument 35. Prism 340 is preferably made of a dispersive material that allows the illumination light to exit at a different point and in a different direction than that of the photon. A Bragg mirror (not shown) that reflects only the illumination light and allows the photon to pass through can be placed between fiber 335 and prism 340, for example, to reflect the illumination light in a direction other than towards prism 340 or even back into the fiber.

[0418] Anti-reflective plates (not shown) can be placed at the input and output of prisms 340 and 345 and adjusted to the wavelength of photon P1.

[0419] We will now describe various ways of implementing the polarization modifier 32 of the system of the figure 1B .

[0420] The polarization modifier 32 preferably includes a polarization direction modifier 32a arranged upstream of a phase modifier 32b.

[0421] In a first example of polarization direction modification, the polarization direction modifier 32a comprises a stack of 560 plates, including quarter-wave plates, oriented differently relative to each other, as illustrated in the figure 5A , such that a circular wave 558 entering one of these quarter-wave plates emerges as a wave 511 linearly polarized along a direction associated with said plate.

[0422] These plates can be designed to function with waves 558 penetrating them in a direction parallel to the bisector of their edges 521 and 522. These plates are preferably composed of uniaxial birefringent crystals such as, for example, rutile. This birefringent crystal can constitute 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 the figure 5A .

[0423] These blades can be placed side by side to form a 524 structure, as illustrated in the figure 5B , so that the outgoing waves 511 or 512 have a linear polarization whose direction of the electric field depends on the point of penetration, in the assembly 524, of two waves 558 or 559 circularly polarized and in a direction parallel to the bisector of the edges 521 and 522.

[0424] Thus, a wave 556 of determined linear direction and polarization entering the quarter-wave plate 551 passes through it in the direction 557 to become circularly polarized before entering a crystal 552 whose refractive index is adjustable, for example under the effect of an electric field generated by electrodes 516, then preferably enters 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 electrodes 516.

[0425] 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. Since the direction of the light ray is different at these locations, the direction of the edges 520 and 521 is preferably different for each element 560 of the assembly 524.

[0426] On the diagram illustrated in the figure 5B , waves 511 and 512 thus constitute two possibilities for the light ray to pass through assembly 524. These waves exit assembly 524 linearly polarized along different directions and having the same direction of propagation but at different locations on the edge 514 of assembly 524. They enter another crystal 554 whose refractive index is electrically adjustable by electrodes 518 and 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 exit crystal 555 as a wave 513 of the same direction at the same location 515.

[0427] Crystals 552, 553, 554, and 555 are, for example, Merck E7 liquid crystals across whose electrodes voltages between 0 and 5000 V are applied, provided the distance between the electrodes of each pair is 5 mm, allowing their refractive indices to vary between 1.5 and 1.67. The electrodes are preferably coated with a dielectric film. Since these refractive indices, modified by electric fields, can differ depending on the relative direction of the electric field of the light and the direction of the electric field, the application of successive perpendicular electric voltages allows the refractive index to be modified for each of the two components of said light, the latter being the superposition of waves whose electric field is perpendicular to the figure 5B and waves whose electric field is perpendicular to the direction of propagation and in the plane of the figure.

[0428] In a second example (not shown) of polarization direction modification, the linearly polarized wave, polarized in a given direction, enters a first quarter-wave plate, transforming its polarization into circular polarization. It then enters a second quarter-wave plate, transforming this circular polarization back into linear polarization along an adjustable direction that depends on the orientation of this second quarter-wave plate. The orientation of the second quarter-wave plate is achieved, for example, by mechanical control of a sensor, or by an electrically controlled device that allows its rotation, for example, by rubbing against a shaft set in motion by a piezoelectric material or by an electric motor, for example, a direct current motor.

[0429] In a third example illustrated at figure 5C Liquid crystals are used to control the rotation of the linear electric field of the incident photons 526, which are linearly polarized along the same polarization direction. For example, they begin by passing, preferably perpendicularly, through one of two transparent electrodes 527 of 0.2 µm 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. They then pass through the liquid crystal 529 over 2 µm before passing through the second transparent electrode 527, whose face 528, preferably parallel to the first electrode, is also coated with a material allowing the liquid crystals to be aligned 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. Applying an electrical voltage, for example, between 0 and 1 V, gradually reorients the liquid crystals to align them with the direction of photon propagation, thereby progressively reducing the difference in refractive index between the two polarizations perpendicular to the photon propagation and the rotational power of the device. This device therefore allows continuous selection of the output direction of the incident photon polarization between 0° and 60°.

[0430] Devices such as the one illustrated in the figure 5B are advantageously used in a device similar to that described above and illustrated in the figure 5A , for example placed between plates 524 and 554, each of, for example, 4 elements 560 allowing the linear polarization of an incident photon to be placed in one of four precise directions, for example -90°, -45°, 0° and +45°, then each of the devices described in the figure 5B placed in succession, and preferably aligned with the direction of propagation of the photons coming out of the 560 devices which precede them, allowing to add to this rotation a rotation of any angle for example between 0 and 45°.

[0431] We illustrated at the figure 6 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 P1 of polarization field E into two electromagnetic waves of linear polarization E1 and E2 on two different axes x1 and x2.

[0432] On the second axis x 2, a delay plate 321 of variable refractive index, for example comprising a Pockels cell such as lithium niobate, controlled by electrodes 322 or a nonlinear material, is placed so as to make the wave E 2 oriented along the second axis x 2 acquire a predetermined phase shift with respect to the wave E 1 oriented along the first axis x 1.

[0433] Another birefringent plate 370, for example made of paratellurite, is arranged at the output of the phase modifier 32b, allowing the two waves whose polarization fields E1 and E2 are perpendicular to be joined along the same x axis into a wave or photon P1 of field E' which has 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 depending on the direction of the electric field of the light with respect 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.

[0434] The measuring instruments 35 of the first receiver 3 can be of various types and comprise different elements. These depend in particular on the nature of the polarization of the photon P1 when it is emitted by the emitter 2. Some examples are illustrated in figures 7 And 8and described below.

[0435] In the example illustrated in the figure 7 , the measuring instrument 35 includes a polarizing filter 350 arranged on the propagation path D1 of the photon P1 and a photon detector 355 arranged on the same propagation path, downstream of the filter 350.

[0436] The 350 polarizing filter only allows photons with a specific linear polarization to pass through, while absorbing those with polarization perpendicular to them. It therefore allows the selection of photons with linear polarization in a particular direction.

[0437] In the example considered, the 350 polarizing filter is a grid made of vertical wires, for example metallic ones. It only allows photons with horizontal linear polarization H to pass through.

[0438] In an illustrated variant at the figure 8 The measuring instrument 35 comprises an anisotropic plate 360, for example a birefringent plate, a birefringent prism, or two birefringent prisms placed side by side. The plate is, for example, made of barium beta borate (BaB₂O₄, BBO).

[0439] The photon P1, whose quantum state is to be measured, reaches plate 360 ​​on an incident propagation path D1, and is transmitted on one of two propagation paths D11 or D12, depending, for example, on whether its polarization is in the plane of plate 360 ​​(that is, perpendicular to the plane of the figure 8 ), or normal to the plane of the 360 ​​blade.

[0440] The measuring instrument 35 further comprises two detectors 355, each placed on a propagation path D11 or D12 of the photon P1.

[0441] In this example, and unlike the polarizing filter, all photons can be detected by the 355 detectors, regardless of their polarization.

[0442] In some embodiments, a quarter-wave plate is placed upstream of the 360 ​​anisotropic plate 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.

[0443] The second receiver 4 can include different types of optical amplifier 40 and measuring instrument 45.

[0444] For example, a doped fiber amplifier, such as the one illustrated in the figure 9 .

[0445] In this example, the amplifier 40 includes a fiber 400, specifically a fiber made of nonlinear material, into which the second photon P2 is introduced after passing through a dichroic prism 451 when it reaches the receiver 4.

[0446] An electromagnetic control wave F used to provide 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.

[0447] The control wave F is preferably of high light intensity and preferably of shorter wavelength than that of the photon P2.

[0448] During its passage through the fiber 400 and under the influence of the luminous flux F, the photon P2 is multiplied into N photons P20. These N photons and the flux F then 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, which allows the polarization of the luminous flux to be determined. Examples of its implementation are given in figure 10A et 10B .

[0449] We can deduce from the measurements of the measuring instrument 45 the information transmitted by the first receiver, because the amplification of the photon P2 by the device 40 preserves its polarization.

[0450] In particular, if photon P2 is the entangled photon of a photon P1 absorbed in one of two known complementary polarizations of the first receiver, the multiplied N photons P20 are measured with a polarization that can be deduced from the absorption polarization of photon P1 using the Jones matrix calculated during a calibration as described above.

[0451] The measuring instrument 45 may comprise a series of semi-reflective blades 452 and a mirror 453, as illustrated in the figure 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 equal intensity. The filters 350 split the luminous flux into two orthogonally polarized luminous fluxes, so that the detectors 455 can either determine the intensity of said flux along 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's slit interferometer.

[0452] Interferometers are preferably arranged so that the light paths of the two orthogonal components are identical, as the light flux resulting from the multiplication of a single photon is very short. Using multiple pairs of orthogonal directions, for example, offset by 45° from each other, advantageously allows for multiple measurements of the polarization—that is, the direction of polarization as well as the phase difference between the two directions—thus enabling greater measurement accuracy.

[0453] There figure 10B This represents an example of such a Young's slit interferometer. Two waves, 460 and 463, originate from the prism 350. Wave 460 passes, for example, through a prism 461, which straightens its direction of propagation so that it becomes parallel to wave 463 at point 462. Wave 463 then passes, for example, through a half-wave plate, which aligns the electric field of wave 465 with that of wave 462. Waves 462 and 465 then pass through two holes drilled in a screen 466 before interfering with each other to form fringes on a screen 467. This screen is observed by a camera or equipped with photosensitive sensors, allowing the position of the brightest fringe on the screen 467 to be determined.

[0454] Information, including binary information, can be transmitted between receivers 3 and 4 of a system 1 such as the one described in the figure 1B , for example by following the steps illustrated in figures 11A et 11B .

[0455] The protocol for matching 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 P1, is determined before the start of the transmission.

[0456] As an example, the selection below consists of not measuring the first photon P1 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.

[0457] 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.

[0458] The emitted photons P1 and P2 exhibit an indeterminate quantum state in a predetermined pair of complementary polarizations, for example a polarization at 45° if they are linearly polarized (the complementary polarizations being 0° and 90).

[0459] At step 11, the photon P1 reaches the optical selector 30 of the receiver 3.

[0460] If a "0" bit is to be transmitted, the photon P1 is, for example, reflected by the optical selector, along a perpendicular path in the example illustrated in the figure 11A (but any other path is possible), so as not to be able to reach the measuring instrument 35. The photon P1 can in particular be trapped at step 12 in a device protecting its quantum state 5, in order to avoid its absorption, at least until the second photon P2 has reached the second receptor 4.

[0461] For example, the P1 photon retains its 45° polarization.

[0462] If a bit "1" is to be transmitted, the photon P1 passes, for example, through the optical selector 30 to head towards the measuring instrument 35, as illustrated in the figure 11B .

[0463] The quantum state of photon P1 is then measured by measuring instrument 35, in step 13.

[0464] The photon P1 now has a definite quantum state, for example, vertical polarization (90°) or horizontal polarization (0°). Instantly, the measurement performed in step 13 projects the entangled photon P2 into a definite state.

[0465] At 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 stream of multiplied photons P20, each photon P20 having retained the polarization of the photon P2.

[0466] In step 16, the polarization of the P20 photon flux is measured by a measuring instrument 45.

[0467] If, on average, an intermediate result is obtained, for example a polarization at 45°, it is deduced that the first photon P1 has not been measured, and a bit "0" is received.

[0468] 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 P1 has been measured, and a bit "1" is received.

[0469] It is still possible to transmit series of discrete values ​​between receivers 3 and 4 of a system 1 such as the one described in the figure 1A , for example by following the steps illustrated in the figure 12 .

[0470] 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.

[0471] At step 17, the photon P1 reaches the polarization modifier 32, which converts the linear polarization of the photon P1 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.

[0472] At step 13, the photon P1 is absorbed by instrument 35 in one of the two complementary states of the selected pair, simultaneously projecting the entangled photon P2 into its complementary state.

[0473] The following steps 15 and 17 are similar to those described above; the polarization of the P2 photon is measured by amplification and then absorption, and the discrete transmitted value is deduced.

[0474] The invention is not limited to the measurement of linear polarization of photons. Other types of quantum states can be measured and / or other measurement methods can be used, including measurements in other observable bases.

[0475] Photons P1 and P2 are emitted, for example, with circular entangled polarization, and the measuring instrument 35 projects, by measuring linear polarization, photon P1 and, by entanglement, photon P2, into a basis of linear polarization.

[0476] Alternatively, the photons P1 and P2 are emitted with linear entangled polarization, and the measuring instrument 35 projects, by measuring a circular polarization, the photon P1 and by entanglement the photon P2, according to this observable basis.

[0477] In another example, photons P1 and P2 are emitted with linear entangled polarization vertically or horizontally and measuring instrument 35 measures linear polarization at 45° or -45° from the vertical or horizontal.

[0478] In one variant, the receiver 3 comprises two measuring instruments 35, one measuring linear polarization, the other measuring circular polarization. The optical selector, for example, sends the photon P1 to the first measuring instrument if a bit "1" is to be transmitted, to the second measuring instrument if a bit "2" is to be transmitted, and prevents it from being measured if a bit "0" is to be transmitted.

[0479] In each of the above examples, the measuring instrument 45 of the second receiver 4 can be configured to detect whether the first photon P1 has been measured, or not, and, if so, with what polarization it was measured at the first receiver.

[0480] Gyroscopes can also be used at emitter 2 and receivers 3 and 4 to determine the polarization direction of photons P1 and P2, if these are emitted and transported to the receivers with linear polarization.

[0481] As mentioned above, receptors 3 and 4, as well as device 5, can be equipped with devices for counting photons during their absorption, and optionally after they have waited for the absorption of their entangled photon, which can be accompanied by a timestamp of their arrival, as illustrated in the figure 13 This can, for example, allow the correspondence between entangled photon pairs and transmitted bits to be controlled.

[0482] Each photon, for example, triggers the timestamping process upon arriving at the receiver in step 80, specifically upon 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 stored in a register R, onto a free memory register M, preferably after subtracting from the arrival time at detector 5D the transit time of the photon in the waiting device 5.

[0483] A similar device (not shown) can be arranged at the second receiver 4.

[0484] Preferably, the clocks enabling the timestamping just described are synchronized for both receivers 3 and 4, which optionally allows for the definition of time intervals for processing photons common to both receivers, and for processing the "multiple" double pairs of photons emitted by emitter 2.

[0485] The second receiver 4 may also include a switch 50 placed in front of the optical amplifier 40, and is configured to absorb or reflect any unwanted photon(s) PE2 that reach the receiver 4 after photon P2 during the same processing time interval, as shown in the figure 14 .

[0486] The switch 50 can also absorb any PA2 photons emitted by the amplifier 40 towards the emitter 2 during signal amplification, or during the de-excitation of molecules or atoms of the amplifying medium.

[0487] 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.

[0488] In some embodiments, the system according to the invention may include several transmitters arranged differently relative to the receivers, in particular to establish bidirectional communication.

[0489] In the example illustrated in the figure 15 , system 1 has two emitters 21 and 22, each emitting pairs of entangled photons towards two receivers 91 and 92.

[0490] Transmitter 21 is closer to receiver 91 than to receiver 92, and transmitter 22 is closer to receiver 92 than to receiver 91. This arrangement allows receivers 91 and 92 to communicate bidirectionally; the photon P11 emitted by transmitter 21 arrives first at receiver 91, which can then act as the first receiver 3, i.e. transmit information to receiver 92 which receives its entangled photon P12 and acts as the second receiver 4.

[0491] Conversely, the photon P21 emitted by the emitter 22 arrives first at the receiver 92, which this time allows the transmission of information to the receiver 91, which receives the entangled photon P22. The mechanism for transmitting information, particularly binary information, is, for example, similar to what was described above, in the figures 11 And 12 .

[0492] Reflecting devices 93 and 94 can be arranged near receptors 91 and 92, respectively, in order to reflect photons possibly reflected by receptors 91 and 92.

[0493] We will now describe, with reference to the figure 16 an implementation variant of the invention, intended to verify that information transmitted by transmitter 2 has not been listened to and, if necessary, to generate a shared key for the exchange of information between receivers 3 and 4, from the transfer of information which is known not to have been listened to.

[0494] The system of the figure 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 polarization direction which corresponds to that expected for the photons which have travelled from the emitter 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 emitting the information to the receiver 4.

[0495] Filter 46 prevents a fraudulent receiver from replacing the genuine receiver 4, from observing the exact polarization of the entangled photon after multiplication of said photon, and then from emitting a fraudulent photon towards the genuine receiver 4, in place of the genuine photon, to be necessarily observed by receiver 4 in the same relative polarization as the genuine photon, because on the one hand, if said photon is not entangled with another photon, its polarization will not change after passing through filter 46 and will therefore have the polarization imposed by filter 46 and not that of the genuine photon, and on the other hand, if the fraudulent photon is entangled with another photon, called a 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 filter 46.if the verification of the relative polarization of its entangled photon is then found to be inadequate by a third-party device.

[0496] It is therefore extremely unlikely that all or some of the photons in a group of entangled photons observed by the two receptors 3 and 4 have been observed elsewhere, if their relative polarizations are always different.

[0497] The equality of the quantum state of the photons used for transmitting information arriving at each of the two receivers 3 and 4 can be statistically verified, and the probability that some of the photons were observed can be deduced to be low, by applying the following method: Upon reception of the photons by each of the receivers 3 and 4, the receivers record the reception time as well as the exact polarization of the photons using photon detectors, and not only which complementary polarization pair they belong to. The times and polarizations of detected photons that are too close to each other to have their polarization or arrival time measured independently are, however, preferably not recorded, and the two receivers 3 and 4 preferably have synchronized clocks.

[0498] After a determined number of photons carrying information I have been received, the second receiver 4 generates a message containing the precise detection time and polarization for each of the photons whose attributes have been noted and retained as transmitting information and therefore belonging to a group of NSP photons or more having a given polarization or the complementary polarization of that polarization; NSP is defined above as the predetermined threshold number of photons received in a given polarization or its complementary polarization allowing the identification of the reception of information.

[0499] This message is signed, preferably using the random hashing technique described in US application 20210165914 A1, by receiver 4, and then sent to receiver 3 with said signature, preferably by implementing a quantum transmission means as described above, and 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 whose 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 to be authentic and the proportion of non-matching polarizations is less than a given threshold, for example 1% if 450 different polarization pairs are used, or a multiple such as 2 of the probability that two different pairs of entangled photons are emitted at times indistinguishable by the receivers.

[0500] Furthermore, a relative polarization in each of the pairs of polarizations of the photons having been retained to have 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 randomly generated key and known only to each of the receivers; the receiver 3 having carried out the verification of the 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 the reception dates of the photons whose relative polarizations did not correspond or whose entangled photon was never received by the receiver 3.

[0501] Thus, in one example, the following steps are implemented. Step 1

[0502] Receiver 4 receives, from transmitter 2, a stream of photons carrying information and establishes a first list of the dates of reception of the photons which were used to determine this information as well as the relative polarization designating which of the two complementary polarizations in which the photon was received. Step 2

[0503] 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 and the signature to receiver 3. Step 3

[0504] Receiver 3 receives the list and the signature and then verifies said signature. Step 4

[0505] Receiver 3 establishes a second list consisting of the elements from the first list whose relative polarizations of the photons received by receivers 3 and 4 are the same, or whose entangled photon never reached receiver 3. Receiver 3 has stored in a register the relative polarization of each photon used for information transmission, as well as its reception date. Knowing the difference in travel time of the entangled photons between emitter 2 and each of the two receivers 3 and 4—that is, the travel time—receiver 3 can determine, for each photon in the first list, the relative polarization of the photon it received at the time of reception of the photon by receiver 4, minus the travel time.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 receptor 3 and a second of these parts containing photons whose two entangled photons have reached their respective receptors but with equal relative polarizations. Step 5

[0506] If the number of elements in the second list limited to pairs of entangled photons, where each of the two photons has reached its respective receiver, is less than the product of a predetermined ratio by counting the elements in the first list limited to pairs of entangled photons, where each of the two photons has reached its respective receiver, then the information is declared to have been transmitted unlistened to. Step 6

[0507] If the information is declared to have been transmitted unlistened to, then the second list is sent signed by receiver 3 to receiver 4, then a third list is created by 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 have been observed to be different.

[0508] Otherwise, if the aforementioned product is above said threshold, a message indicating that the transmission is likely to have been listened to is sent by receiver 3 to receiver 4. Step 7

[0509] Upon receipt of the second list by receiver 4 and after verification of the signature, the third list is recreated in receiver 4 using the first and second lists, then a signed message, confirming the good receipt of the second list, is sent by receiver 4 to receiver 3. Step 8

[0510] 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.

[0511] In another example, the following procedure can be implemented to verify that an information message I has not been listened to.

[0512] The first receiver 3 can establish a first list containing the dates of reception at the first receiver and a second list containing these dates of reception and the polarization states of the photons absorbed by the first receiver 3, and the second receiver 4 can establish a third list containing the dates of reception at the second receiver 4 and a fourth list containing these dates of reception and the polarization states of the photons received by the second receiver.

[0513] 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.

[0514] Upon receipt of the third and / or first list, respectively, the first receiver 3 and / or the second receiver 4 can establish a fifth list containing 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.

[0515] If only one of the two receivers establishes the fifth list, said fifth list may be transmitted, preferably electronically signed, to the other receiver, such that the first receiver 3 and the second receiver 4 can respectively establish a sixth list and a seventh list of polarization states of 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 ttra and marked on the fourth list.

[0516] The respective signatures of the sixth list and the seventh list can then be exchanged between the first and second receivers according to the process corresponding to the third variant of the message integrity verification process, the first receiver 3 being the first device, the sixth list being the first dataset, the second receiver 4 being the second device and the seventh list being the second dataset.

[0517] There figure 19 This illustrates an example of a process for creating electronic signatures of a dataset Sd. In step o, a dataset, for example, composed of the bits of the relative polarizations of entangled photons P1 or P2 received at receivers 3 or 4, is created. In step i, a secret number R is concatenated to the dataset to form a modified dataset. In step ii, a hash of the modified dataset is calculated. And in step iii, the hash is encrypted using a one-time key K, for example, by an XOR operation.

[0518] Comparing 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 photons have been lost in the transmission channel.

[0519] 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 one can, for example, extract one-time keys or lists of random rotation angles of polarization measurement bases.

[0520] In another example, illustrated in the figure 17 , a physical protection of the second propagation path D2 is used for a portion Ltot of the second propagation path D2 ending at the second receiver 4, where the photons P2 propagate from the emitter 2 after their entangled photons P1 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 length Ltra.

[0521] The portion Ltot is long enough that the difference t between the travel time t tot of a photon P2 in said portion Ltot and the travel time t tra of 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 potentially being listened to by a third party.

[0522] This prevents a hacking device placed in this unprotected portion of the propagation path from listening in and retransmitting the photons that propagate there when they are no longer entangled.

[0523] In another example, illustrated on the figure 18Two polarization rotators 80 and 90 are placed upstream of the two photon receivers 3 and 4, respectively. The two photon rotators change the polarization direction of the photons synchronously and randomly, for example by 45° or 0°, for example all photons or one photon out of two, so that a spying 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°.

[0524] This prevents a known secret number from being generated by a hacker replacing the entangled photon emitter with a photon emitter sending pairs of non-entangled photons representing a message that is also meant to be sent by the first receiver.

Claims

1. Method of transmitting a message M by quantum communication from a first receiver (3) to a second receiver (4) with eavesdropping detection, the transmission and detection method comprising the steps of: (A) generating a series of Np pairs of entangled photons (P1; P2) from an emitter (2), the first photon (P1) of each pair being emitted toward the first receiver (3) on a first propagation path (D1) and the second photon (P2) of the pair being emitted simultaneously toward the second receiver (4) on a second propagation path (D2), the first and second photons (P1; P2) being entangled, the second receiver (4) being located on the propagation path of the second photon (P2) further away 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 ttra, (B) converting the message M into a series of Ni pieces of information I to be transmitted in a first predetermined numbering base, (C) at the first receiver (3), for each piece of information I: (a) for each entangled photon (P1), modifying the polarization state of the first photon (P1) 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 among at least two different pairs of complementary absorption polarizations, and (b) by using an absorption instrument (31), absorbing the first photon (P1) in one of the two complementary polarizations of the selected pair, (D) at the second receiver (4): (a) duplicating each received photon (P2) to form a flux of multiplied photons by using an amplification device (40), the light that is created having preserved the polarization state of the photon, (b) measuring, for each photon duplicated, the average polarization state of the light flux, and (c) determining according to this measurement the polarization state of the first entangled photon (P1) received by the first receiver (3), in order to deduce therefrom the information I that may 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 that may have transmitted the information I, (E) performing an eavesdropping detection method, (F) deducting from the deduction list the transmitted message M, the eavesdropping detection method performed at step (E) comprising a shared quantum key generation method comprising the following steps: (G) the first receiver (3) establishing a first list comprising the reception dates at the first receiver (3) and a second list comprising these reception dates and the relative polarization states of the photons (P1) absorbed by the first receiver (3), and the second receiver (4) establishing a third list comprising the reception dates at the second receiver (4) and a fourth list comprising these reception dates 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 reception of the third list and / or the first list, respectively, the first receiver (3) and / or the second receiver (4) establishing a fifth list comprising the dates at which the first photons (P1) were received at the first receiver (3), for the pairs for which the two entangled photons (P1; P2) were received at both receivers (3; 4), as some photons may have been lost during the transmission between the emitter (2) and one or both 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), the first receiver (3) and the second receiver (4) establishing, respectively, a sixth list and a seventh list of relative polarization states of the photons (P1) 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 (P1) 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 (P1) received at the same time and marked on the second list, each relative polarization state on the seventh list of a photon (P1) entangled to 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 ttra and marked on the fourth list, (K) 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 deduction list of information I is considered non-eavesdropped.

2. Method according to Claim 1, the relative polarization of a photon (P1; P2) being the polarization of the photon (P1; P2), or a bit assigned to all the possible polarizations that can be taken by the second entangled photons (P2) after the first photon (P1) has reached the first receiver (3) where 1 is said assigned bit of a photon entangled to a photon to which a 0 has been assigned.

3. Method according to Claim 1 or 2, wherein the comparison method in step (K) comprises the steps of: i. the first receiver (3) mixing a first secret number, shared or to be shared with the second receiver (4), called mixer number, with the sixth list, using a mixing function, in order to obtain a first mixed data, ii. the first receiver (3) hashing the first mixed data using a hash function, iii. the first receiver (3) encrypting the hashing of the first mixed data with a second secret number shared or to be shared with the second receiver (4), iv. the first receiver (3) sending to the second receiver (4) the encrypted hashing of the first mixed data with the second secret number, v. the second receiver (4) receiving the data sent by the first receiver (3) at step iv, vi. the second receiver (4) decrypting the received data, vii. the second receiver (4) mixing the first secret number with the seventh list, using a mixing function, in order to obtain a second mixed data, viii. the second receiver hashing the second mixed data using a hash function, ix. the second receiver comparing the hashing 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 used again or changed periodically such as each time or every day, and / or the second secret number being kept secret and used again or changed periodically such as each time or every day, and / or 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.

5. Method according to either one of Claims 3 and 4, the receivers (3; 4) sharing the secret numbers before step (K) takes place or after step (K) takes place and prior to their use, notably the receivers (3; 4) sharing the secret number by sending it to each other encrypted with a one-time key, and / or a mixer number identifier possibly being exchanged between the first receiver (3) and the second receiver (4), which are each able to find the corresponding mixer number in a memorized list of mixer numbers, and / or the mixing function being an XOR logic function, or a suffix function, consisting in adding the mixer number to the end of the sixth list, or an encrypting function using the mixer number as encryption key to encrypt the sixth list, or the mixing function being a combination of an XOR function, a suffix function consisting in adding the mixer number to the end of the first dataset and an encryption function using the mixer number as encryption key to encrypt the first dataset, the encrypting function being for example an XOR function, in particular the transmitted message M being used as an encryption key if the deduction list has been considered as not having been eavesdropped, and / or the encryption keys generated during the transmission and detection method and / or made of the message M being used, if the deduction list has been considered non-eavesdropped, as first and / or second secret numbers.

6. Method according to any one of Claims 3 to 5, a signed message being exchanged after step ix. between the two receivers (3; 4) before the sixth and seventh lists are used as one-time keys, and / or the deduction list being considered as not having been eavesdropped if the two data compared at step ix. are equal.

7. Method according to any one of the preceding claims, the lists established at step (G) being established for the transmission of a single piece of information I or established using photons (P1) transmitted for the transmission of a series of multiple pieces of information I, and / or the second propagation path (D2) being physically protected against eavesdropping, at least for a portion (Ltot) of the second propagation path (D2) ending at the second receiver (4), where the photons (P2) travel from the emitter (2) after their entangled photons (P1) have been received by the first receiver (3), the portion (Ltot) being preferably long enough so that the difference t between the travel time ttot of a photon (P2) in said portion (Ltot) and the travel time (ttra) of the photon (P2) in the non-entangled state toward the second receiver (4) may be detected by the second receiver (4) and that this detection enables the second receiver (4) to mark any incoming message as being potentially eavesdropped by a third party, and / or two polarization rotators (80; 90) being placed ahead of the two photon receivers (3; 4) respectively, the two photon rotators modifying the direction of polarization of the photons synchronously and randomly by 45° or 0° so that a spy photon emitter may not know the polarization directions that are being measured by the receivers (3; 4).

8. Method according to any one of the preceding claims, the sixth list and the seventh list being made of bits, and potentially being used as a shared list of random bits, and / or the first receiver (3) coding the same information I on many successive incoming photons (P1), as some of their entangled photons (P2) may be lost before reaching the second receiver (4), and / or the first receiver (3) reserving a piece of information I0 to be used to separate the sending of any other two pieces of information I, notably if these two other pieces of information I are the same, representing for instance the same letter, and / or the step (F), consisting in deducting from the deduction list the transmitted message M, being carried out by the first receiver (3) having coded a separation letter between any two equal successive letters of the message M, accounting for the travel time ttra and the fifth list, taking out of the deduction list the polarizations of photons for which the first entangled photon never reached the first receiver, to create a cleared deduction list, and the second receiver (4) deducting from the cleared deduction list the message M that was transmitted, or the second receiver (4) counting as received information any information that is recorded successively on the deduction list more than a preset number of times within a preset number of successively received pieces of information I, and / or the message M being considered as not having been eavesdropped if the deduction list has been considered as non-eavesdropped.

9. Method according to any one of the preceding claims, the pair of complementary absorption polarizations being selected from among at least three different pairs of complementary absorption polarizations, notably from among at least 210 distinct pairs of complementary absorption polarizations, and / or a plurality of pairs of entangled photons (P1; P2) being generated successively by the emitter (2), each pair of photons making it possible to transmit a piece of information I from the first receiver (3) to the second receiver (4).

10. Quantum communication system (1) implementing the method described in any one of the preceding claims, comprising: • an emitter (2) of entangled photons (P1; P2), comprising a source configured in order 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 (D1), • a first receiver (3) arranged on the first propagation path (D1), comprising a complex absorber (31) configured to absorb the photon (P1) in a polarization state selected from among 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 (P1) has reached the first receiver (3), said second receiver comprising: - an optical amplifier (40) to multiply the second photon (P2) while preserving its polarization, and - arranged downstream of the amplifier (40), a measuring instrument (45) to measure the average polarization of the multiplied photons, the complex absorber (31) preferably being configured to absorb the photon (P1) in a predetermined polarization state selected from among the states of at least three different pairs of complementary polarizations, the complex absorber (31) notably comprising: - at least one instrument (35) 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 (P1) to the selected polarization along which said instrument (35) absorbs the photons.

11. System according to the preceding claim, the polarization modifier (32) comprising a polarization direction modifier (32a) arranged upstream of a polarization phase modifier (32b), the polarization direction modifier (32a) in particular comprising two quarter-wave plates arranged one after the other on the propagation path (D1) of the first photon (P1), the orientation of at least one of the two plates being variable, or the polarization direction modifier (32a) comprising a plate or a prism made of chiral or rotating material inducing rotation of the polarization by an angle dependent on the location through which the wave enters said chiral or rotating material.

12. System according to the preceding claim, the polarization phase modifier (32b) comprising a birefringent first plate or prism splitting the beam into two electromagnetic waves with a linear polarization, one along a first axis and the other along a second axis, and a retardation plate with a variable refractive index arranged on the second axis.

13. System according to any one of Claims 10 to 12, said at least one instrument (35) comprising at least one filter to send the first photon toward one or the other of two photon detectors according to the polarization state of the first photon.

14. System according to any one of Claims 10 to 13, the measuring instrument (45) of the second receiver (4) comprising at least one photon detector (455) arranged to measure the polarization of the light originating from the multiplication of the second photon (P2) and / or the measuring instrument (45) of the second receiver (4) comprising a succession of semi-reflective plates (452) arranged downstream of the optical amplifier (40), said plates (452) directing the flux of multiplied photons with an equal intensity toward a first phase measurement instrument, this being a polarization measuring instruments arranged in order to measure the intensity of the flux along two perpendicular axes, a second phase measurement instrument measuring the phase shift of the light between these two same axes, and a third phase measurement instrument measuring the phase shift of the light between the bisector of the same axes and an axis perpendicular to that bisector, the first semi-reflective plate diverting for example a third of the light flux toward the first phase measurement instrument, the second semi-reflective plate diverting for example half of its incoming light flux toward the second phase measurement instrument and the remaining half of its incoming light flux toward the third phase measurement instrument.

15. System according to any one of Claims 10 to 14, the optical amplifier (40) being a doped-fibre amplifier, and / or the emitter (2) being configured to successively generate a plurality of pairs of entangled photons (P1; P2), and / or the emitter (2) and each of the receivers (3; 4) comprising a clock, the clocks of the emitter (2) and of the receivers (3; 4) being synchronized with one another, and / or the second receiver (4) comprising a switch (50) arranged in front of the optical amplifier (40) and configured to absorb or reflect the photon or photons subsequent to a first photon reaching said second receiver (4) in a predetermined time interval, and / or comprising a second emitter capable of generating one or more pairs of entangled photons, the second emitter being located closer to the second receiver (4) than to the first receiver (3).