METHOD FOR SECURELY TRANSMITTING QUANTUM STATES BETWEEN A MULTIPLE OF ONLINE PARTICIPANTS VIA A QUANTUM COMMUNICATION CHANNEL

Description

[0001] The present invention relates generally to the field of quantum communication and more particularly to a method and a device for exchanging sequences of quantum states between several participants in the same quantum communication channel.

[0002] Quantum communication involves exchanging quantum states, encoded on quantum bits or qubits, between multiple participants. When the quantum states to be exchanged must be exchanged secretly, quantum communication is coupled with quantum cryptography methods, the latter consisting of using the properties of quantum physics to establish cryptography protocols, i.e., protocols that ensure the confidentiality of the exchanged data, making quantum communication secure.

[0003] A well-known example of a quantum communication protocol is quantum key distribution (QKD), which allows two participants connected by an insecure quantum communication channel to establish a random key that can be used to encrypt standard classical communication. In a quantum key distribution protocol, there are two participants, usually playing different roles: a sender, who sends quantum information in the form of qubits, and a receiver, who decodes this information using a suitable device.

[0004] It is known to those skilled in the art, in quantum key distribution protocols used in practice, to encode the qubits constituting the key to be distributed in photons. The generation of the photons is carried out by a laser, the encoding of the photons is carried out by an optical properties modulator, and the decoding by the receiver by an assembly involving a photon detector. At the end of the protocol, the transmitter and the receiver share a secret chain of random qubits, see for example US5764765.

[0005] The article "Quantum key distribution with hacking countermeasures and long term field trial" by AR Dixon et al., in SCIENTIFIC REPORTS, vol. 7, no. 1, May 16, 2017 (2017-05-16), DOI: 10.1038 / S41598-017-01884-0, presents a countermeasure using a portion of the power to detect an attack, this defends against attacks including blinding attacks.

[0006] A technical problem that the invention proposes to solve is to propose a secure method for the exchange of a flow of quantum states between two participants among a number of participants of the same quantum communication channel greater than or equal to three and forming a quantum communication chain, the two participants exchanging a flow of quantum states which may be different from the participants called transmitter and receiver in a quantum key distribution protocol of the prior art, as well as a device for implementing this method, said device using simple and very limited hardware.

[0007] In order to solve this problem, the applicant has developed a secure transmission method according to claim 1 and a device according to claim 8. Further details are set out in the dependent claims.

[0008] The advantages and particularities of the present invention will result from the detailed description which follows, given by way of non-limiting example and made with reference to the appended figures: - There figure 1 illustrates several examples of degrees of freedom for encoding quantum bits as well as examples of associated incompatible bases. - The figure 2 is a synopsis of the method for secure transmission of a quantum state between two participants in a communication chain comprising N online participants according to a first embodiment. - The figure 3 illustrates an example of the effect of transformations that can be applied to a reference quantum state as part of the process for secure transmission of sequences of quantum states. - The figure 4 illustrates an example of implementing a covert channel attack in an optical quantum communication device. - The figure 5 illustrates an additional step carried out in a second embodiment of the method for secure transmission of a quantum state. - The figure 6 illustrates a device implementation for the secure transmission method of a sequence, for a quantum communication chain of 4 participants. - The figure 7 illustrates a temporal location modulating device - The figure 8 is an example of incompatible bases in a 4-dimensional Hilbert vector space. DETAILED DESCRIPTION

[0009] The present invention presents a secure transmission method for sending sequences of quantum states, encoded on quantum bits, between several online participants on a quantum communication channel. In the embodiments and examples presented below, the quantum bits are encoded with photons in a degree of freedom thereof. By photon degree of freedom is meant a physical property described by quantum mechanics and usable for quantum communications. Examples of photon degrees of freedom are phase, phase difference, frequency, polarization or temporal localization. In this description, the formalism that represents a quantum state in the form of a vector |α> in a Hilbertian vector space of dimension d is used.The concept of Hilbertian vector space extends the methods of linear algebra by generalizing the notions of Euclidean space (such as the Euclidean plane or the usual 3-dimensional space) and Hermitian space to spaces of any dimension (finite or infinite). A vector |α> of a Hilbertian vector space of dimension d can be described by means of a basis of the Hilbertian vector space of dimension d. For the remainder of the description of the embodiments and examples that follow, the concept of incompatible bases will be used. Two bases of the same Hilbertian vector space are said to be incompatible if each vector of one of the two bases has projections of equal lengths onto each of the vectors of the other basis. The . figure 1 gives examples of incompatible bases for different photon degrees of freedom, in a 2-dimensional Hilbert vector space.

[0010] A first embodiment of the invention is described here in the particular case of a Hilbertian vector space of dimension d, d being an integer greater than or equal to 2, and in the case of a communication chain comprising N online participants C 1 , ... C i ,...C j ... and CN , where C 1 is the sending participant and CN is the receiving participant, and where N is an integer greater than or equal to 3. figure 2 illustrates this first embodiment. The intermediate participants C 2 to C N-1 are called transformers. The term "transmitter" refers to a participant equipped with a suitable device capable of sending quantum information, in particular quantum bits encoding quantum states. Here, since it is considered that the quantum bits are encoded in photons, the device available to the transmitter is a laser generating photons. The term "receiver" refers to a participant equipped with a suitable device capable of decoding the quantum information sent by a transmitter, in particular measuring a quantum state linked to a received quantum bit. In the case where the quantum bits are encoded in photons, the device available to the receiver may be a single photon detector SPD.The term "transformer," in the case where quantum bits are encoded in photons, refers to a participant equipped with hardware that allows it to modulate the optical signal it receives. A transformer is considered to have limited hardware and can only modulate the optical signal it receives, but neither create a signal itself nor measure the quantum state of a photon it receives.

[0011] In the secure transmission method described in this application, two distinct participants C i and C j among the participants C 1 to CN of the communication chain, Ci being the most upstream participant in the communication chain, C j the most downstream in the communication chain, decide to share a sequence of Q quantum states qq , for q an integer between 1 and Q, said sequence having a light power P seq in number of photons per second. Depending on the nature of the participants C i and C j , the secure transmission method may have differently ordered steps. Also, the participants C i and C j are known to all, that is to say to the other participants in the communication chain but also to the public.

[0012] In particular, according to the invention, the succession of the following steps, the method can be schematized as an iterative process for each from q=1 to Q, comprising at each iteration:a first action performed by the transmitter C1 comprising the preparation by the transmitter C1 of a photon in a starting quantum state |u> of an orthonormal encoding basis Ba of dimension d and basis states |e 0 >, |e 1 >,... |e d-1 >, with a chosen at random between 0 and 1, transmission of the prepared photon in the communication chain, a second action performed by the first participant Ci on said photon, of decision of transformation or not of the quantum state of the transmitted photon, into an orthogonal basis quantum state in the encoding basis B 0 and in the encoding basis B 1 a third action performed by the second participant C j on said photon, of decision of transformation or not of the quantum state of the photon received from the immediately preceding participant C j-1 into a corresponding orthogonal quantum state in the encoding basis B 0 and in the encoding basis B 1 a fourth action performed by the receiver CN including measurement,in the standard basis B 0 or in the basis B 1 , of the final state |final alpha > of the photon transmitted in the communication chain by the receiver CN, exchange on a classical communication channel between at least some of the participants, of at least some of the decisions among those of the starting basis a, of the starting state |u>, of the measurement basis chosen by said receiver CN and of the result of the measurement of |final alpha > in this measurement basis, obtaining, between the first and second participants Ci and Cj, a description of the transmitted quantum state qq corresponding to one of the basic states |e 0 >, |e 1 >,... |e d-1 >, thanks to said part of the decisions and said result of the measurement; ,

[0013] Then, when the Q iterations have been carried out, the reconstruction, by the first and second participants Ci and Cj, by concatenation, of a sequence of the descriptions of the Q quantum states transmitted qq , for q ranging from 1 to Q.

[0014] According to a first embodiment, the transmitter C1 performs a first action which comprises the following steps: Choose a value sq equal to 0 or 1 Choose a value I between 0 and d-1 Apply a transformation P sq< X l to a reference photon created by the transmitter at the start of the communication chain

[0015] The first participant Ci then performs a second action which includes the following steps: Choose a value m between 0 and d-1 Apply a transformation X m to the photon received through the communication chain,

[0016] The second participant C j performs a third action, which includes the following steps: Choose a value n between 0 and d-1 Apply a transformation X n to the photon received through the communication chain,

[0017] The receiver, finally, performs a fourth action, which includes the following steps: Choose a tq value equal to 0 or 1 Apply a transformation P (-1)tq< to the photon received through the communication chain,

[0018] Then, an exchange is carried out on a conventional communication channel between at least some of the participants, of at least some of the decisions among those of the starting base a, of the starting state |u>, of the measurement base chosen by said receiver (CN) and of the result of the measurement of |alpha final> in this measurement base.

[0019] This exchange allows each of the first and second participants to obtain information from the transmitter and receiver of the other participant.

[0020] This information includes a description of the transmitted quantum state qq corresponding to one of the basis states |e 0 >, |e 1 >,... |e d-1 >, thanks to the said part of the decisions and the result of the measurement;

[0021] One advantage of this embodiment is that the transmitter and receiver operations are traditionally used in the absence of other participants on the communication line, i.e., on currently deployed quantum communication networks, to establish shared encryption keys. Thus, intermediate participants can be added to posteriori on already deployed quantum communication architectures without modifying the transmitter and receiver operations, thus extending the capabilities of said architecture.

[0022] Below, another embodiment will be described. The explanations related to this embodiment and the described variants are provided without loss of generality and may apply, mutatis mutandis, to the first embodiment previously described.

[0023] In this second embodiment, we consider here a first case of a method for secure transmission of a sequence of quantum states where the participants Ci and C j are different participants from the participants C 1 and CN , that is to say that they are neither transmitter nor receiver, but simply transformers. N is then an integer greater than or equal to 4. The figure 2 gives a general illustration of this method of secure transmission of a sequence of quantum states. The steps of the method of secure transmission of the sequence of quantum states can then consist of the repetition of the following steps, for q being an integer between 1 and Q: in a first action, the transmitting participant C 1 sends through the communication chain a prepared photon in a reference quantum base state |0> of a working encoding base B 0 called standard base, orthonormal, of dimension d, and orthogonal base states |0>, |1>,... |d-1>: the first participant Ci performs a second action which can be seen as composed of two successive steps G 1 and G 2 upon reception of the photon transmitted in the communication chain, more precisely: ■ in a first step G 1 , the first participant Ci decides whether or not to transform the quantum state of the received or generated photon into a quantum base state |m> orthogonal to the state |0> in the encoding base B 0 , ■ in a second step G 2 , the first participant Ci decides whether or not to apply a transformation P allowing a change of encoding base to be made, from the standard base B 0 to an orthonormal encoding base B 1 of dimension d,incompatible with the standard basis B 0 , of orthogonal basis states |e 0 >, |e 1 >,... |e d-1 > ; the photon from the second step G 2 is propagated in the communication chain; the second participant C j performs a third action which can be seen as composed of two successive steps G 3 and G 4 upon receipt of the photon transmitted in the communication chain, more precisely: ■ in a third step G 3 , the second participant C j decides whether or not to apply the inverse transformation of the transformation P, noted P (-1)< , allowing a change of encoding basis to be made, from the encoding basis B 1 to the standard basis B 0 ; ■ in a fourth step G 4 ,the second participant C j decides whether or not to transform the quantum state of the photon received from participant C j-1 into a corresponding orthogonal quantum state in the encoding basis resulting from step G 3; the photon from the fourth step G 4 is propagated in the communication chain; the receiver CN detects and measures in the standard basis B 0 the state |final alpha > of the photon transmitted in the communication chain. the first and second participants C i and C j exchange with each other on a classical communication channel their decisions of transformation of encoding bases resulting from the second and third steps G 2 and G 3; the first and second participants C i and C j obtain a description of the quantum state qq corresponding to one of the basis states |0>, |1>,... |d-1>, thanks to the encoding basis information exchanged between and to the measurement of the final state |final alpha >. ,

[0024] Examples of classic communication channels are Ethernet connections, Wi-Fi, or TCP / IP protocols.

[0025] After the Q repetitions have been performed, the first and second participants C i and C j reconstruct, by concatenation, a sequence of descriptions of the Q quantum states qq .

[0026] It will now be described on the one hand, what is meant by the term "description of a quantum state qq", and on the other hand how the transmission of the sequence of quantum states is secured by the protocol described in the previous case. The first and second actions carried out by the first and second participants C i and C j transcribe a method of applying the principle of conjugate coding. Conjugate coding consists of encoding information in a quantum state while keeping secret the basis in which this information is coded. This principle is based in particular on the use of two bases for encoding a Hilbertian vector space that are incompatible with each other. Taking into account a quantum state in one of the two bases, this state, if measured in a corresponding incompatible basis, will behave in a completely random manner.Indeed, the definition given above of two incompatible bases, that is to say, that the projection of each vector of one of the two bases has projections of equal lengths on each of the vectors of the other base can be formulated mathematically in the following way, taking the example of bases B 0 and B 1 previously mentioned:.

[0027] For m and n integers between 0 and d-1: 〈 m | e n 〉 = 1 d And 〈 e m | n 〉 = 1 d where <..|..> denotes the scalar product of the Hilbert vector space defining the state vectors.

[0028] In quantum mechanics, the quantities |<m | e n > | 2< and |< em | n >| 2< represent respectively the probabilities of finding a system in an initial state |en > in the state |m>, if one were to carry out a measurement in the standard basis B 0 , and of finding a system in an initial state |n> in the state |em >, if one were to carry out a measurement in the incompatible basis B 1 . Thus, these probabilities are all equal. It can therefore be concluded that the measurement, in the corresponding incompatible basis, of a state prepared in either of the bases B 0 or B 1 would give a completely random measurement result.

[0029] Thus, in the method of secure transmission of a sequence of Q quantum states, only two configurations allow a quantum state transmission providing relevant information, that is, a result of the measurement by the receiver CN that can be used by the first and second participants C i and C j: this is either the case where the first and second participants C i and C j both decide during the second and third steps G 2 and G 3 to apply respectively the transformations P and P (-1) < , or the case where neither of them decides during the second and third steps G 2 and G 3 to apply the transformation P, respectively P (-1) < . Indeed, in these two cases, the third step G 3 makes it possible to undo the transformation carried out during the second step G 2 and to return to the basis B 0 , in which the measurement made by the receiver CN will give a non-random measurement result.The state measured by the receiver CN will be that resulting from the transformations resulting from the first and fourth steps G 1 and G 4 . Thus, the security of the method of transmitting the sequence of quantum states comes from the fact that the state measured by the receiver CN is that of the succession of transformations resulting from the first and fourth steps G 1 and G 4 , but does not make it possible to determine the state, chosen by the first participant Ci during the sub-step G 1 , transmitted to the second participant C j . This is masked by the combination of the first and second actions carried out respectively by the first participant Ci and the second participant C j .

[0030] In the case where the first participant Ci decides to apply the transformation P during the second step G 2 , and the second participant C j decides not to apply the transformation P (-1)< during the sub-step G 3 , or conversely, in the case where the first participant Ci decides not to apply the transformation P during the sub-step G 2 , and the second participant C j decides to apply the transformation P (-1)< during the third step G 3 , the information which will have circulated in the communication chain and measured by the receiver CN will not be relevant, that is to say, the result of the measurement carried out by the receiver CN will not be able to be used by the first and second participants Ci and C j . Indeed, it will correspond to a measurement of a state of a basis B 0 or B 1 in the corresponding incompatible basis, and, as explained previously, to a completely random result.In practice, this result of the transmission of the corresponding quantum bit will be discarded and set aside.

[0031] This is why the term "description of a quantum state qq" is used to generalize the result of the measurement made by the CN receiver because the quantum information deduced from this measurement is not necessarily relevant and does not necessarily correspond to the nature of the state qq.

[0032] Thus, depending on the decisions taken by the first and second participants C i and C j , information coded in a quantum bit can be transmitted from the first participant Ci to the second participant C j in a secure manner because the other participants, different from C i and C j , only have access, when the receiver CN announces the measurement of the final state, to the information relating to the final alpha state of the photon transmitted in the communication chain. From a statistical point of view, on average, and due to configurations where the quantum information relating to the final alpha state is random and therefore irrelevant, one quantum state out of two can be transmitted by the first participant Ci to the second participant C j in a manner hidden from the other participants in the communication chain.

[0033] Here we consider a second case where the first participant Ci is the transmitting participant C 1 but the participant C j is only a transformer, different from the receiver CN . N is then an integer greater than or equal to 3. The steps of the secure transmission method of the sequence of quantum states can then consist of repeating the following steps, for q being an integer between 1 and Q: the transmitter C 1 performs the first action described in the first case and composed of the first and second successive steps G 1 and G 2 ; the photon resulting from the second step G 2 is propagated in the communication chain ; the second participant C j performs the second action described in the first case and composed of the third and fourth successive steps G 3 and G 4 ; the photon resulting from the fourth step G 4 is propagated in the communication chain ; the receiver CN detects and measures in the standard basis B 0 the final state |alpha > of the photon transmitted in the communication chain. the transmitter C 1 and the second participant C j exchange between them on a classical communication channel the encoding bases resulting from the steps G 2 and G 3 ; the transmitter C 1 and the second participant C j obtain a description of the quantum state qq corresponding to one of the basis states |0>, 11 >,...|d-1>, thanks to the basic encoding information exchanged between and the measurement of the final state |final alpha >. .

[0034] After the Q repetitions have been performed, the transmitter C 1 and the second participant C j reconstruct, by concatenation, a sequence of descriptions of the Q quantum states qq , discarding, if necessary, the irrelevant and unusable descriptions.

[0035] We consider here a third case where the first participant Ci is a transformer, different from the transmitter C 1 , and the participant C j is the receiver CN , and where N is an integer greater than or equal to 3. The steps of the method for secure transmission of the sequence of quantum states can then consist of the repetition of the following steps, for q being an integer between 1 and Q: the transmitter C 1 sends through the communication chain a photon prepared in a quantum state of reference basis |0> of a working encoding basis B 0 called standard basis, orthonormal and of dimension d, and of orthogonal basis states |0>, |1>,...|d-1>: the first participant Ci performs the first action described in the first case and composed of the first and second successive steps G 1 and G 2 ; the photon from the second step G 2 is propagated in the communication chain; the receiver CN detects the photon it receives, performs the second action described in the first case and composed of the third and fourth successive steps G 3 and G 4 , then measures in the standard basis B0 the final state |alpha > of the photon from the fourth step G 4 ; the first participant Ci and the receiver CN exchange between them on an encrypted classical communication channel the encoding bases resulting from the second and third steps G 2 and G 3 ; the first participant Ci and the receiver CN obtain a description of the quantum state qq corresponding to one of the basis states |0>, |1>,... |d-1>, thanks to the encoding base information exchanged between and to the measurement of the final state |alpha >.

[0036] After the Q repetitions have been performed, the first participant Ci and the receiver CN reconstruct, by concatenation, a sequence of descriptions of the Q quantum states qq , discarding, if necessary, the irrelevant and unusable descriptions.

[0037] We consider here a fourth and final case where the first participant Ci is the transmitter C 1 and the second participant C j is the receiver CN , and where N is an integer greater than or equal to 3. The steps of the method for secure transmission of the sequence of quantum states can then consist of the repetition of the following steps, for q being an integer between 1 and Q: the transmitter C 1 performs the first action described in the first case and composed of the first and second successive steps G 1 and G 2 ; the photon from the second step G 2 is propagated in the communication chain ; the receiver CN detects the photon that it receives, performs the second action described in the first case and composed of the third and fourth successive steps G 3 and G 4 , then measures in the standard basis B 0 the state |final alpha > of the photon from step G 4 ; the transmitter C 1 and the receiver CN exchange between them on an encrypted classical communication channel the encoding bases resulting from steps G 2 and G 3 ; the transmitter C 1 and the receiver CN obtain a description of the quantum state qq corresponding to one of the basis states |0>, |1>,... |d-1>, thanks to the encoding base information exchanged between and to the measurement of the final state |final alpha >.

[0038] After the Q repetitions have been carried out, the transmitter C 1 and the receiver CN reconstruct, by concatenation, a sequence of descriptions of the Q quantum states qq , discarding, if necessary, the irrelevant and unusable descriptions.

[0039] For the second, third and fourth cases previously described, the principle of securing the transmission of sequences of quantum states through the communication chain of the N participants and the concept of descriptions of quantum states are the same as those described for the first case of secure transmission.

[0040] The first and second actions performed respectively by the first and second distinct participants C i and C j in the four different cases of secure transmission of sequences of quantum states will now be formally described.

[0041] We consider a Hilbert vector space for encoding quantum states of dimension d. The first action carried out, during the q-th repetition of the succession of steps previously described by participant Ci, can thus consist of the following steps: the first participant C i chooses a value sq equal to 0 or 1 the first participant C i chooses an integer value m between 0 and d-1 the first participant C i applies a transformation P sq< X m to the photon received through the communication chain, or in the case where i is equal to 1, to the photon at the beginning of the communication chain, where, it is recalled, the notation P designates a transformation allowing a change of encoding base to be made, from the standard base B 0 to an encoding base B 1 orthonormal, ie for m an integer between 0 and d-1: P|m〉=em and where the notation X m denotes the following transformations, respectively in the base B 0 and base B 1 , for m and t two integers between 0 and d-1: Xm|t>=|t+mmodd> And Xm|et>=|et+mmodd> where the abbreviation mod denotes the mathematical function modulo.

[0042] The transformation X m corresponds to the first step G 1 , and the transformation P sq< corresponds to the second G 2 . The effect of the first action performed by the first participant Ci, P sq< X m , on a reference state |0> is illustrated in the figure 3 . The states |+> and |-> are defined as follows: | + > = 1 2 | 0 > + | 1 > | − > = 1 2 | 0 > − | 1 >

[0043] The second action carried out, during the q-th repetition of the succession of steps previously described by the second participant C j can thus consist of the following steps: the second participant C j chooses a value tq equal to 0 or 1; the second participant C j chooses a value n between 0 and d-1; the second participant C j applies a transformation X n P (-1)tq< to the photon received through the communication chain where the notation P (-1) designates the transformation allowing a change of encoding base to be made, from the incompatible base B 1 to standard base B 0 , ie for m an integer between 0 and d-1: P−1|em>=|m> and where: the notation P (-1)0< means that the transformation P (-1)< does not take place; the notation P (-1)1< means that the transformation P (-1)< takes place,

[0044] The transformation P (-1)tq< corresponds to the third step G 3 , and the transformation X n corresponds to the fourth step G 4 .

[0045] Thus, in both configurations allowing quantum state transmission providing relevant information, i.e. either the configuration where participants C i and C j both decide in the second and third steps G 2 and G 3 to apply respectively the transformations P and P (-1)< , or the configuration where neither decides in the second and third steps G 2 and G 3 to apply respectively the transformations P and P (-1)< , the resulting encoding basis in step G 4 is the standard basis B 0 . The final state |alpha final > is equal to |m+n mod d> and can be measured in the standard basis B 0 by the receiver CN . The result of the measurement announced by the receiver is m+n mod d. All participants ignorant of the value of m and n, i.e. all participants except the first and second participants C i and C j learn nothing about the value m+n mod d.The transformation X has the effect of masking the state transmitted by the first participant C i when it is measured and announced by the receiver CN . Due to the disclosure of the measurement result by the receiver CN , m+n mod d, the participant C j can thus deduce the state |m> transmitted to it by the participant C i . The transmission of the quantum state by the first participant C i to the second participant C j was indeed carried out securely, because all the other participants in the chain only know the result m+n mod d of the measurement carried out by the receiver C n .

[0046] Thus, the application of conjugate coding through the use of incompatible encoding bases allows a secure transmission of a quantum state, or quantum information, between two first and second participants Ci and Cj, in which the transmitted quantum state is unknown to the other participants in the communication chain.

[0047] More generally, it can be envisaged that the transmission of quantum states by the first participant Ci to the second participant C j is repeated to transmit a plurality of messages. In this case, Ci can send a posteriori to C j the decisions that it has taken at the different repeated second steps, and C j can select the information from measurements for which it has taken correct decisions during the different repeated third steps G3.

[0048] More theoretically, behind the use of conjugate coding lies the use of the uncertainty principle of quantum physics. The use of conjugate bases has the effect that reading information coded in another base in one base gives a completely random value. This is maximum incompatibility, because we speak of incompatibility as soon as there is uncertainty about the value sent.

[0049] In the other two configurations not allowing a quantum state transmission providing relevant information, that is, as explained above, in the case where participant Ci decides to apply the transformation P during sub-step G 2 , and participant C j decides not to apply the transformation P (-1)< during sub-step G 3 , or conversely, in the case where participant Ci decides not to apply the transformation P during sub-step G 2 , and participant C j decides to apply the transformation P (-1)< during sub-step G 3 , the result of the measurement announced by the receiver CN will be random and discarded and set aside.

[0050] According to one embodiment of the method for secure transmission of a sequence of quantum states, the dimension d of the Hilbertian vector space for coding the state vectors is equal to 2.

[0051] According to one embodiment of the invention, countermeasure mechanisms may be implemented to prevent third parties from learning the modulations made by the intermediate participants and thus learning the secret information exchanged.

[0052] In particular, one possible attack involves injecting light with a given characteristic (wavelength, polarization, and time) and measuring it after passing through an intermediate participant in order to learn its modulation characteristics.

[0053] To avoid this attack, filters can be implemented. Since the modulators already have polarization filtering characteristics, one can simply add a frequency filter, in order to let through only light at a given frequency, and a time gate in order to let through only photons at given times (corresponding to transmissions by the transmitter C 1 ).

[0054] This strategy works by imposing constraints on the optical signals transmitted by the transmitter C 1 .

[0055] The frequency filter can be implemented, for example, by a Fabry-Perot etalon, and the time gate can be an electro-optical intensity modulator, for example similar to that implemented by the C 1 transmitter.

[0056] Therefore, the only possible attacks would be to inject light with the same characteristics as those intended by the system. This is only possible by using a beam splitter.

[0057] The use of a beam splitter would inevitably lead to a decrease in optical power. In addition, a splitter does not allow the recovery of the light injected by the adversary because it cannot be distinguished from the "legitimate" beam transmitted by the transmitter. This decrease and disruption of the optical flow can be detected, for example, by the mechanism described below.

[0058] Another embodiment of the first case of secure transmission, where the first and second participants C i and C j are different participants from the participants C 1 and CN , that is to say that they are neither transmitter nor receiver, but simply transformers and that the communication chain comprises a number N of participants greater than or equal to 4, will be described, where the second and fourth steps G 2 and G 4 can be followed by complementary steps aimed at preventing spy attacks on the transmission of quantum states by covert channels.

[0059] During the q-th repetition of the succession of steps of the method for secure transmission of a sequence of Q quantum states qq , step G 2 is followed by the following successive steps: during a fifth step G 5 , a portion P seq1 of the light power coming from participant C i-1 can be taken; during a sixth step G 6 , the portion P seq1 can be compared with a portion P seq1' of the light power P seq of the sequence of photons sent by the transmitter C 1 , in order to detect a potential injection of spy photons between participant C i-1 and the first participant C i .

[0060] Step G 4 can also be followed by the following successive steps: during a seventh step G 7 , a portion P seq2 of the light power coming from participant C j-1 can be taken; during an eighth step G 8 , the portion P seq2 can be compared with a portion P seq2' of the light power P seq -P seq1 , in order to detect a potential injection of spy photons between participant C j-1 and the second participant C j .

[0061] Indeed, it can be considered that, since the first and second participants C i and C j are transformers that cannot measure light power, a spy applies the following attack: in the case of quantum bits encoded in the photon phase, the spy could inject between the emitter C 1 and the participant Ci photons of polarization different from those emitted by the emitter C 1 , which is a legitimate participant. figure 4 shows an example of how this covert channel attack on a first participant C i can be carried out by a spy in an optical quantum communication device. The spy would simply have to combine his spy photons with the photons legitimately emitted by the transmitter C 1 , for example using a polarization combiner, and recover the spy photons he has introduced just after participant Ci. Thus, the spy could measure the modulation applied by the first participant C i , and learn, for example, the values ​​of sq and m chosen by the first participant Ci. The same attack of injecting spy photons upstream of the second participant C j and recovering modulated photons by the second participant C j just after the second participant C j could be applied. A necessary condition for carrying out this type of attack is for the spy to be able to position himself just before and just after a participant.Thus, this type of attack is not possible on the sending C 1 and receiving CN participants. The . figure 4 schematically illustrates the principle of covert channel attack as described previously.

[0062] The light power samples taken during the fifth and seventh steps G 5 and G 7 allow the measurement and verification of the conformity of these measurements, by the comparisons made during the sixth and eighth steps G 6 and G 8 , with the light power P seq sent by the transmitter C 1 . These samples and comparisons thus constitute countermeasures carried out respectively by the first participant Ci and the second participant C j . The figure 5 schematically illustrates the principle of countermeasure which can be carried out by one of the first or second participants C i or C j during the sixth and eighth steps G 6 or G 8 .

[0063] The fifth, sixth, seventh and eighth steps G 5 to G 8 therefore constitute an additional security of the method of transmitting a sequence of quantum states between the first and second participants C i and C j , because they make it possible to detect possible attacks by hidden channels by spies. This additional security can be implemented with simple and inexpensive hardware.

[0064] In this embodiment, the uncertainty principle also ensures security. Suppose that a spy measures the photons of the first participant Ci and re-emits a photon identical to the one he measured. If he measured in an encoding base different from that chosen by the first participant C i , which happens half the time, then the spy will modify the photon, due to the equiprobability of the measurement results that he will be able to obtain. The statistics will be modified accordingly in a visible way for the first participant Ci and the second participant C j . By comparing a small portion of the photons received with those sent, the first and second participants C i and C j , can thus spot a spy who is listening to their conversation.

[0065] Thus this additional security mechanism can operate independently of the frequency filter and the time gate described above, but it also allows a synergistic effect since each of these two mechanisms targets complementary attacks and their joint use thus allows blocking a wide range of possible attacks.

[0066] According to one embodiment, these two additional mechanisms are implemented jointly.

[0067] Preferably, the degree of freedom of the photons encoding the quantum bits is chosen from the phase, the phase difference, the temporal location, the polarization or the frequency of the photon.

[0068] Advantageously, the sequence of Q quantum states qq for q integer between 1 and q is chosen randomly in order to establish a quantum key distributed between the participants Ci and Cj. In this particular case, the step of exchanging the transformation decisions of steps G 2 and G 3 corresponds to the “key sifting” operation carried out in a standard manner in a quantum key distribution protocol.

[0069] The implementation of the method for secure transmission of a sequence of Q quantum states qq, q being an integer between 1 and Q can be carried out using a device comprising: a laser capable of generating photons and an initial modulator capable of modulating a degree of freedom of a generated photon, said laser and said initial modulator being associated with the transmitter C 1 N-2 intermediate modulators capable of modulating a degree of freedom of a received photon, each of the N-2 intermediate modulators being associated with an intermediate participant C k , among the N-2 intermediate participants C 2 to C N-1 distinct from the transmitter C 1 and the receiver CN a photon detector capable of detecting single photons and a final modulator capable of modulating a degree of freedom of a received photon; said photon detector and said final modulator being associated with the receiver CN There figure 6 illustrates an implementation of this device for a four-participant communication chain.

[0070] The device previously described can be used in the following manner. Once the first and second participants C i and C j have been chosen, a laser associated with the transmitter C 1 generates, following a command from the transmitter C 1 , a stream of photons encoding a quantum bit sequence. The stream of photons is transmitted in the communication chain via the initial modulator, the N-2 intermediate modulators, the final modulator, and up to the photon detector.

[0071] In the context of the transmission of a sequence of Q quantum states coded on Q photons, for each photon: during the transmission of said photon through the communication chain, the first participant Ci performs on said photon a first action, comprising a first decision step G 1 and a second decision step G 2 , by controlling a modulator associated with it, that is to say either the initial modulator or one of the N-2 modulators, following the first action of the first participant Ci on said photon, the transmission of the photon is continued to the second participant C j , which performs on the photon, after reception thereof, a second action, comprising a third decision step G 3 and a fourth decision step G 4 , by controlling a modulator associated with it, that is to say either one of the N-2 intermediate modulators or the final modulator.Following the second action of the second participant C j on the photon, the transmission of said photon is continued until its reception by the photon detector associated with the receiver CN , the receiver CN measures the final state of the quantum bit coded in the photon that it receives and shares the result of the measurement with the other participants in the communication chain, the first and second participants C i and C j exchange on a conventional communication channel the decisions taken during the second and third steps G 2 and G 3 , the first and second participants C i and C j deduce a description of the quantum state using the exchanged decisions and the measurement by the receiver CN of the final state of the quantum bit coded in the photon detected by the photon detector associated with the receiver CN . .

[0072] Thus, the first participant C i and the second participant C j reconstruct, by concatenation, a sequence of descriptions of the Q quantum states transmitted, discarding, if necessary, the irrelevant and unusable descriptions, in the cases previously described.

[0073] The advantage of the method for transmitting sequences of quantum states between several participants presented in this application is therefore that it can be implemented by a device comprising only a single laser and a single photon detector. These latter components being generally the most expensive hardware elements, the protocol presented here therefore makes it possible to carry out a transmission of sequences of quantum states with a lower cost per participant.

[0074] In the case previously described where the first and second participants C i and C j are different participants from the participants C 1 and CN , the device previously described can be supplemented by: a first beam splitter Si positioned upstream of the modulator associated with the first participant C;, a first photodiode PD i associated with the first participant C i and capable of measuring a light power, a second beam splitter S j positioned upstream of the modulator associated with the second participant C j , a second photodiode PD j associated with the second participant C j and capable of measuring a light power.

[0075] The beam splitter Si separates the photon flux received from participant C i-1 in two distinct directions, one towards the modulator of the first participant C i then towards the rest of the communication chain, the other towards the photodiode PD i . The second beam splitter S j separates the photon flux received from participant C j-1 in two distinct directions, one towards the modulator of the second participant C j then towards the rest of the communication chain, the other towards the second photodiode PD j . These additional components enable the implementation of securing the method for transmitting quantum state sequences against covert channel attacks. In particular, they enable the fifth, sixth, seventh and eighth steps G 5 to G 8 previously described to be carried out. The fifth and seventh steps G 5 and G 7 are carried out respectively by measuring the light power P seq1 by the photodiode PD i and by measuring the light power P seq2 . The sixth and eighth comparison steps G 6 and G 8 are carried out using the measurements of the light powers P seq1 and P seq2 and the light power prediction values ​​P seq1' and Ps eq2' . For example, when one of the comparisons, between P seq1 and P seq1' on the one hand, and between P seq2 and P seq2' on the other hand, results in an inequality, an attack by a spy, for example by photon injection, can be detected.In this configuration, the first and second beam splitters Si and S j are configured so that with a probability p, the photons passing through them are directed towards the first and second photodiodes PD i and PD j respectively. The photodiodes PD i and PD j can measure the average light power over a given period of time. Thus, these additional components are also much simpler and less expensive compared to hardware conventionally used in quantum communication devices such as, for example, single-photon detectors.

[0076] When the degree of freedom of photons to encode quantum bits is phase, the initial modulator, the N-2 intermediate modulators and the modulator can be phase modulators. For example, the LN53S-FC or LN65S-FC model marketed by Thorlabs can be used.

[0077] When the degree of freedom of photons to encode quantum bits is the polarization of photons, the initial modulator, the N-2 intermediate modulators and the modulator can be polarization modulators. For example, a model of the PSC-LN series of products marketed by the iXblue Photonics company can be used.

[0078] When the degree of freedom of photons to encode quantum bits is the temporal localization of photons, the initial modulator, the N-2 intermediate modulators and the modulator can each comprise a number d of delay lines and a number 2d of splitter blades, where d represents the dimension of the Hilbert vector space representing quantum states. The superposition of temporal localizations to be achieved to create an incompatible basis can be obtained by programming the splitter blades. figure 7 illustrates a time location modulator device, in the case where d is equal to 2.

[0079] There figure 8 shows an example of a pair of incompatible bases designed in the case where the degree of freedom of the photons is the localization for a Hilbert vector space of dimensions 4. The four time localizations corresponding to the states of the basis |t 0 >, |t 1 >, |t 2 > and |t 3 > are t 0 , t 1 equal to t 0 +τ, t 2 equal to t 0 +2τ and t 3 equal to t 0 +3τ. An example of an incompatible basis can then be the basis |τ 0 >, |τ 1 >, |τ 2 > and |τ 3 > as represented in figure 8 A use of these two bases is found in the article “Provably secure and high-rate quantum key distribution with time-bin qubits” (Islam et al., Sci. Adv. 2017;3).

[0080] Post-processing such as error correction or standard confidentiality amplification in quantum key distribution protocols can also be applied following the implementation of the different embodiments of the method for secure transmission of sequences of quantum states.

[0081] According to certain embodiments, the invention may have several advantages: the method of transmitting quantum states can be doubly secure, on the one hand intrinsically by the application of the principle of conjugate coding, on the other hand extrinsically by the countermeasure implemented to detect attacks by hidden channels; the material used for the implementation of the presented transmission method is simple and inexpensive because it requires only two expensive components, a laser and a single photon detector, as well as other much more accessible components, modulators, delay lines, splitter plates, classic photodiodes.

[0082] According to embodiments of the invention, it is possible to connect different devices, in order to form larger-scale transmission networks.

[0083] Thus, each device as previously described can cover a geographical area of ​​moderate size, corresponding for example to an urban or metropolitan area (of the MAN type for “ Metropolitan Area Network "). These networks can be connected together on a national or international scale at interconnection points whose function is to transmit keys from one network to another. These network interconnections can, for example, be made through satellite networks, allowing metropolitan networks to be interconnected.

Claims

1. A method for secure transmission of a sequence of Q quantum states qq encoded in the form of a sequence of Q photons, q being an integer between 1 and Q, between a first participant (Ci) and a second participant (Cj), chosen from a plurality of N distinct participants (C1), ....(Ci), ...(Cj), ...(CN) of a single quantum communication channel forming a communication chain between a transmitter (C1) and a receiver (CN), where N is an integer greater than or equal to 3, wherein the first participant (Ci) is located upstream of the second participant (Cj) in the communication chain, said method comprising, in order: - the following sequence of steps, repeated from q=1 to Q: ∘ a first action performed by the transmitter (C1) comprising the preparation by the transmitter (C1) of a photon in a starting quantum state |u> of an orthonormal encoding base Ba of dimension d and base states |e0>, |e1>,... |ed-1 >, with a chosen at random between 0 and 1, ∘ transmitting the prepared photon in the communication chain, ∘ a second action performed by the first participant (Ci) on said photon, of deciding whether or not to transform the quantum state of the transmitted photon into an orthogonal base quantum state in the encoding base B0 and in the encoding base B1 ∘ a third action performed by the second participant (Cj) on said photon, of deciding whether or not to transform the quantum state of the photon received from the immediately preceding participant (Cj-1) into a corresponding orthogonal quantum state in the encoding base B0 and in the encoding base B1 ∘ a fourth action performed by the receiver (CN) comprising the measurement, in the standard base B0 or in the base B1, of the final |alphafinal> state of the photon transmitted in the communication chain, ∘ exchanging over a conventional communication channel between at least some of the participants, of at least some of the decisions among those of the starting base a, the starting state |u>, the measurement base chosen by said receiver (CN) and the result of the measurement of |alphafinal> in this measurement base, in order to enable each of said first and second participants to obtain information from said transmitter, from said receiver and from the other of said first and second participants, ∘ obtaining, between the first and second participants (Ci) and (Cj), a description of the transmitted quantum state qq corresponding to one of the base states |e0>, |e1>,... |ed-1>, thanks to said part of the decisions and said measurement result; - then, reconstituting, by the first and second participants (Ci) and (Cj), by concatenation, of a sequence of descriptions of the Q transmitted quantum states qq, for q ranging from 1 to Q, and wherein i is different from 1 and N, and j is different from 1 and N, the sequence of Q photons encoding the sequence of Q quantum states qq has a given light power Pseq and N is an integer greater than or equal to 4, and wherein: - Said second action includes: ∘ a step (G5) of sampling a first portion P(seq1) of the light power (Pseq) of the photon stream received from the participant (Ci-1) immediately preceding the first participant (Ci), ∘ a step (G6) of comparing the first portion P(seq1) with a second portion (Pseq1') of the light power (Pseq) of the photon stream sent by the transmitter (C1) in order to detect a potential injection of spy photons before the first participant (Ci), - said third action includes: ∘ a step (G7) of sampling a third portion (Pseq2) of the light power of the photon stream received from the participant (Cj-i) immediately preceding the second participant (Cj), ∘ a step (G8) of comparing the third portion (Pseq2) with a fourth portion (Pseq2') of the difference between the light power of the photon stream sent by the transmitter (Pseq) and the first portion (Pseq1) in order to detect a potential injection of spy photons before the second participant (Cj).

2. The method according to the preceding claim, wherein, for each repetition from q=1 to Q of the succession of steps: - The first action, performed by the transmitter (C1), comprises the following steps: ∘ Choosing a value sq equal to 0 or 1 ∘ Choosing a value I between 0 and d-1 ∘ Applying a PsqXl transformation to a reference photon created by the transmitter at the start of the communication chain - the second action, carried out by the first participant (Ci), comprises the following steps: ∘ Choosing a value m between 0 and d-1 ∘ Applying an Xm transformation to the photon received through the communication chain, - the third action, carried out by the second participant (Cj), comprises the following steps: ∘ Choosing a value n between 0 and d-1 ∘ Applying a transformation Xn to the photon received through the communication chain, - the fourth action, carried out by the receiver (CN), comprises the following steps: ∘ Choosing a value tq equal to 0 or 1 ∘ Applying a transformation P(-1)tq to the photon received through the communication chain, wherein: the notation P1 means that the transformation P takes place, the notation P° means that the transformation P does not take place, the notation P(-1)1 means that the transformation P(-1) takes place, the notation P(-1)0 means that the transformation P(-1) does not take place, the notation Xm designates a transformation from the basic quantum state |t>, t being an integer between 0 and d-1, to the orthogonal state cl(t+m) mod d> in the base B0, or the transformation from a |et> state to d|et+m mod d> in the base B1, for m an integer between 0 and d-1, and c and d global phases induced by these transformations.

3. The secure transmission method according to claim 1, wherein, for each repetition from q=1 to Q of the succession of steps: - the first action comprises the preparation by the transmitter (C1) of a photon in a reference base quantum state |0> of an orthonormal encoding base B0, called the d-dimensional standard base, - the second action carried out by the first participant (Ci) comprises the following steps: ∘ Choosing a value sq equal to 0 or 1 ∘ Choosing a value m between 0 and d-1 ∘ Applying a PsqXm transformation to the photon received through the communication chain, or in the case where i is equal to 1, to the photon at the start of the communication chain, - the third action, carried out by the second participant (Cj), comprises the following steps: ∘ Choosing a value tq equal to 0 or 1 ∘ Choosing a value n between 0 and d-1 ∘ Applying an XnP(-1)tq transformation to the photon received through the communication chain, wherein: - the notation P1 means that the transformation P takes place, - the notation P° means that the transformation P does not take place, - the notation P(-1)1 means that the transformation P(-1) takes place, - the notation P(-1)0 means that the transformation P(-1) does not take place, - the notation Xm designates a transformation from the base quantum state |t>, t being an integer between 0 and d-1, in the orthogonal state |(t+m) mod d> in the base B0, or the transformation from a state |et> to |et+m mod d> in the base B1, for m an integer between 0 and d-1.

4. The secure transmission method according to one of claims 1 to 3, wherein said dimension d is equal to 2.

5. The method according to one of the preceding claims, wherein said photon is transmitted through a frequency filter and a time gate.

6. The secure transmission method according to one of claims 1 to 5, wherein each quantum state qq is encoded in a degree of freedom of the photon chosen from phase, phase difference, temporal localization, polarization or photon frequency.

7. The secure transmission method according to one of claims 1 to 6, wherein the sequence of Q quantum states qq is randomly selected for the purpose of establishing a quantum key.

8. A device for implementing the secure transmission method according to one of claims 1 to 5, or 7, comprising: - a laser capable of generating photons and an initial modulator capable of modulating a degree of freedom of a generated photon, - N-2 intermediate modulators capable of modulating a degree of freedom of a received photon, - a photon detector capable of detecting single photons and a final modulator capable of modulating a degree of freedom of a received photon, wherein: - the laser and the initial modulator are associated with the transmitter (C1) and are able to be controlled by the transmitter (C1), - each of the N-2 intermediate modulators is associated with an intermediate participant (Ck) among the N-2 intermediate participants (C2) to (CN-1) distinct from the transmitter (C1) and receiver (CN) and is controllable by said intermediate participant (Ck), - the photon detector and the final modulator are associated with the receiver (CN) and are controllable by the receiver (CN), and further comprising, in the case where the first participant (Ci) and the second participant (Cj) are both two distinct transmitters (C1) and receivers (CN): - a first beam splitter (Si) positioned upstream of the modulator associated with the first participant (Ci), - a first photodiode (PDi) associated with the first participant (Ci) and able to measure the luminous power of a photon stream, - a second beam splitter (Sj) positioned upstream of the modulator associated with the second participant (Cj), - a second photodiode (PDj) associated with the second participant (Cj) and suitable for measuring a luminous power of a photon stream, wherein: - the first beam splitter (Si) is able to split a photon stream received from the participant immediately preceding the first participant in the communication chain (Ci-1) in two distinct directions, one towards the modulator of the first participant (Ci) and then towards the rest of the communication chain, and the other towards the first photodiode (PDi), - the second beam splitter (Sj) is capable of splitting a photon stream received from the participant immediately preceding the second participant in the communication chain (Cj-1) in two distinct directions, one towards the modulator of the second participant (Cj) and then towards the rest of the communication chain, and the other towards the second photodiode (PDj), in order to implement the secure transmission method according to claim 1.

9. The device for implementing a secure transmission method according to claim 8, wherein: - The degree of freedom of the chosen photon is the phase - The initial modulator, intermediate modulators and final modulator are phase modulators.

10. The device for implementing the secure transmission method according to claim 8, wherein: - The degree of freedom of the chosen photon is polarization - The initial modulator, intermediate modulators and final modulator are polarization modulators.

11. The device for implementing the secure transmission method according to claim 8, wherein: - The degree of freedom of the chosen photon is the temporal localization - The initial modulator, the intermediate modulators and the final modulator each comprise a number of delay lines equal to the size of the quantum bit encoding base and a number of splitter blades equal to twice the number of delay lines.