The present application is a filing under 35 U.S.C. 371 as the National Stage of International Application No. PCT/EP2020/074576, filed Sep. 3, 2020, entitled “METHOD FOR SECURELY TRANSMITTING SEQUENCES OF QUANTUM STATES BETWEEN A PLURALITY OF ONLINE PARTICIPANTS OVER A QUANTUM COMMUNICATION CHANNEL,” which claims priority to France Application No. 1909839 filed with the Intellectual Property Office of France on Sep. 6, 2019, both of which are incorporated herein by reference in their entirety for all purposes.
The present invention generally relates to the field of quantum communication and more particularly to a method and a device for exchanging sequences of quantum states between several participants of the same quantum communication channel.
Quantum communication consists in exchanging quantum states, encoded on quantum bits or qubits, between several participants. When the quantum states to be exchanged should be exchanged secretly, quantum communication is coupled with quantum cryptography methods, these consisting in using the properties of quantum physics to establish cryptography protocols, i.e. which ensure the confidentiality of the exchanged data, allowing securing the quantum communication.
An example of a well-known quantum communication protocol is quantum key distribution (QKD), which enables two participants connected by an insecure quantum communication channel to establish a random key which could be used to encrypt a standard conventional communication. In a quantum key distribution protocol, there are two participants generally playing a different role: an emitter, who sends quantum information in the form of qubits, and a receiver, which decodes this information using an appropriate device.
In quantum key distribution protocols used in practice, a person skilled in the art knows how to encode the qubits forming 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 a modulator of optical properties, and the decoding by the receiver by a bench involving a photon detector. At the end of the protocol, the emitter and the receiver share a secret chain of random qubits.
A technical problem that the invention aims to solve is to propose a secure method for the exchange of a flux 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 stream of quantum states which might be different from the so-called emitter and receiver participants 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.
In order to solve this problem, the Applicant has developed a method for securely transmitting a sequence of Q quantum states qq encoded in the form of a sequence of Q photons, q being an integer comprised between 1 and Q, between a first participant and a second participant, selected amongst a plurality of N distinct participants of the same quantum communication channel forming a communication chain between an emitter and a receiver, where N is an integer greater than or equal to 3, wherein the first participant is located upstream of the second participant in the communication chain,
By the expression communication chain, it should be understood a succession of participants connected to each other. More specifically, the participant C1 is connected to the participant C2; for i comprised between 2 and N−1, the participant Ci succeeds and is connected to the participant Ci−1, and precedes and is connected to the participant Ci+1; the participant CN−1 precedes and is connected to the last participant CN.
In particular, according to one embodiment, for each repetition from q=1 to Q of the succession of steps
According to another embodiment of the invention, for each repetition from q=1 to Q of the succession of steps:
A particular embodiment is that where the dimension d of the encoding base is equal to 2.
According to one embodiment, the photon is transmitted through a frequency filter and a time gate.
In an embodiment of the secure transmission method described in this application, where the number of participants N is greater than or equal to 4, where the first and second participants are neither emitter, or receiver, and where the sequence of Q photons encoding the sequence of the Q quantum states has a given light power, the second step of deciding whether to apply or not a transformation P allowing performing a change of the encoding base, from the standard base B0 into an encoding base B1 incompatible with the standard base B0 is immediately followed by:
In an embodiment of the secure transmission method, the fourth step of deciding whether to transform or not the quantum state of the received photon into a corresponding orthogonal quantum state in the encoding base resulting from the third step is immediately followed by:
Advantageously, each quantum state is encoded in a degree of freedom of the photon selected amongst the phase, the phase difference, the temporal location, the polarisation or the frequency of the photon.
Advantageously, in the secure transmission method according to the invention, the sequence of Q quantum states is randomly chosen in order to establish a quantum key.
Another object of the present invention is a device for implementing the previously-described secure transmission method, comprising:
Advantageously, the laser and the initial modulator are associated to the emitter and are adapted to of be controlled by the emitter. Advantageously, each of the N−2 intermediate modulators is associated to an intermediate participant among the N−2 intermediate participants other than the emitter and the receiver and is adapted to be controlled by said intermediate participant. Advantageously, the photon detector and the final modulator are associated to the receiver and are adapted to be controlled by the receiver.
Thus, the connection between the N participants of the communication chain could be achieved by the transmission of a photon generated by the laser associated to the emitter through the initial modulator, the N−2 intermediate modulators, the final modulator, up to the photon detector associated to the receiver.
In a variant of the previously-described device, the latter may further comprise, in the case where the first participant and the second participant are both distinct from the emitter and the receiver:
This variant of the device allows implementing the embodiment of the secure transmission method in which the fifth, sixth and seventh steps take place.
Advantageously, the first beam splitter is adapted to separate a flux of photons received from the participant immediately preceding the first participant in the communication chain in two distinct directions, one towards the modulator associated to the first participant then towards the rest of the communication chain, the other towards the first photodiode. Advantageously, the second beam splitter is adapted to separate a flux of photons received from the participant immediately preceding the second participant in the communication chain in two distinct directions, one towards the modulator associated to the second participant then towards the rest of the communication chain, the other towards the second photodiode.
In the case where the degree of freedom of the photon encoding the quantum state is the phase of this photon, the initial modulator, the N−2 intermediate modulators and the final modulator may consist of phase modulators.
In the case where the degree of freedom of the photon encoding the quantum state is the polarisation of this photon, the initial modulator, the intermediate modulators and the final modulator may consist of polarisation modulators.
In the case where the degree of freedom of the photon encoding the quantum state is the time location of this photon, each of the initial modulator, the intermediate modulators and the final modulator may comprise a number of delay lines equal to the dimension d of the encoding base of the quantum bits and a number of splitter plates equal to twice the number of delay lines
Other advantages and features of the present invention will arise from the following detailed description, given as a non-limiting example and made with reference to the appended figures:
The present invention presents a method for secure transmission for sending sequences of quantum states, encoded on quantum bits, between several online participants over a quantum communication channel. In the embodiments and examples presented hereinbelow, the quantum bits are encoded with photons within a degree of freedom thereof. By photon degree of freedom, it should be understood a physical property described by quantum mechanics and usable for quantum communications. Examples of degrees of freedom of photons are the phase, the phase difference, the frequency, the polarisation or even the temporal location. In this description, the formalism that represents a quantum state in the form of a vector |α> in a Hilbert vector space with a dimension d is used. The concept of Hilbert vector space extends the methods of linear algebra by generalising the notions of Euclidean space (such as the Euclidean plane or the usual 3-dimensional space) and of Hermitian space to spaces of any dimension (finite or infinite). A vector |α> of a d-dimensional Hilbert vector space could be described by means of a base of the d-dimensional Hilbert vector space. For the following description of embodiments and examples that follow, the concept of incompatible bases will be used. Two bases of the same Hilbert vector space are said incompatible if each vector of one of the two bases has projections of equal length on each of the vectors of the other base.
A first embodiment of the invention is described herein in the particular case of a Hilbert vector space with a dimension d, d being an integer greater than or equal to 2, and in the case of a communication chain comprising N online participants C1, . . . Ci, . . . Cj . . . and CN, where C1 is the emitter participant and CN is the receiver participant, and where N is an integer greater than or equal to 3.
In the secure transmission method described in this application, two distinct participants Ci and Cj among the participants C1 to CN of the communication chain, Ci being the participant furthest upstream in the communication chain, Cj the one furthest downstream in the communication chain, decide to share a sequence of Q quantum states qq, for q an integer comprised between 1 and Q, said sequence having a light power Pseq in number of photons per second. Depending on the nature of the participants Ci and Cj, the secure transmission method may have steps in a different order. Also, the participants Ci and Cj are known to everyone, i.e. to the other participants in the communication chain but also to the public.
In particular, according to the invention, the succession of the following steps, the method may be schematised as an iterative process for each from q=1 to Q, including at each iteration:
Then, when the Q iterations have been performed, the reconstitution, 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.
According to a first embodiment, the emitter C1 performs a first action which comprises the following steps:
The first participant Ci then performs a second action which comprises the following steps:
The second participant Cj performs a third action, which comprises the following steps:
The receiver, finally, performs a fourth action, which comprises the following steps:
Then, an exchange is performed on a conventional communication channel between at least part of the participants, of at least part of the decisions among those of the start base a, of the start state |u>, of the measurement base chosen by said receiver (CN) and of the result of the measurement of |alphafinal> in this measurement base.
This exchange enables each of the first and second participants to obtain information from the emitter, from the receiver of the other participant.
This information comprises 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 the result of the measurement;
One of the advantages of this embodiment is that the operations of the emitter and of the receiver are commonly 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 could be added a posteriori on already deployed quantum communication architectures without modifying the operations of the emitter and of the receiver, thereby extending the capabilities of said architecture.
Below, another embodiment will be described. The explanations related to this embodiment and the described variants are provided without losing sight of generality and could apply, mutatis mutandis, to the first embodiment described before.
In this second embodiment, a first case of a method for securely transmitting a sequence of quantum states is considered herein where the participants Ci and Cj are participants different from the participants C1 and CN, i.e. they are neither emitter nor receiver, but mere transformers. N is then an integer greater than or equal to 4.
Examples of conventional communication channels are Ethernet connections, Wifi, or TCP/IP protocols.
After the Q repetitions have been performed, the first and second participants Ci and Cj reconstitute, by concatenation, a sequence of the descriptions of the Q quantum states qq.
It will now be described on the one hand, what should be understood by the term “description of a quantum state qq”, and on the other hand how securing the transmission of the sequence of quantum states by the protocol described in the previous case is carried out. The first and second actions performed by the first and second participants Ci and Cj transcribe a method for applying the principle of conjugate encoding. Conjugate encoding consists in encoding information in a quantum state while keeping the base in which this information is encoded secret. This principle is based in particular on the use of two encoding bases of a Hilbert vector space that are incompatible with each other. Taking into account a quantum state in one of the two bases, this one, if measured in a corresponding incompatible base, will behave in a completely random manner. Indeed, the definition given above of two incompatible bases, i.e. the projection of each vector of one of the two bases has projections of equal length on each of the vectors of the other base could be mathematically formulated as follows, taking the example of aforementioned bases B0 and B1:
For m and n integers comprised between 0 and d−1:m|en
=1/√{square root over (d)} [Math. 1]
andem|n
=1/√{square root over (d)} [Math. 2]
where < . . . | . . . 22 refers to the scalar product of the Hilbert vector space of definition of the state vectors.
In quantum mechanics, the quantities |<m|en>|2 and |<em|n>|2 respectively represent the probabilities of finding a system in an initial state |en> in the state |m>, if a measurement is made in the standard base B0, and of finding a system in an initial state |n> in the state |em>, if a measurement is performed in the incompatible base B1. Thus, all these probabilities are equal. Hence, it could be concluded that the measurement, in the corresponding incompatible base, of a state prepared in either of the bases B0 or B1 would give a completely random measurement result.
Thus, in the method for securely transmitting a sequence of Q quantum states, only two configurations enable a quantum state transmission providing relevant information, i.e., a result of the measurement by the receiver CN that could be used by the first and second participants Ci and Cj: this is either the case where both the first and second participants Ci and Cj decide during the second and third steps G2 and G3 to respectively apply the transformations P and P(−1), or the case where neither of the two decides during the second and third steps G2 and G3 to apply the transformation P, respectively P(−1). Indeed, in these two cases, the third step G3 allows undoing the transformation performed during the second step G2 and returning to the base B0, wherein the measurement done by the receiver CN will give a non-random measurement result. The state measured by the receptor CN will be that one resulting from the transformations derived from the first and fourth steps G1 and G4. Thus, securing the method for transmitting the sequence of quantum states originates from the fact that the state measured by the receiver CN is that of the succession of the transformations derived from the first and fourth steps G1 and G4, but does not allow determining the state, chosen by the first participant Ci, during the sub-step G1, transmitted to the second participant Cj. The latter is masked by the combination of the first and second actions performed respectively by the first participant Ci and the second participant Cj.
In the case where the first participant Ci decides to apply the transformation P during the second step G2, and the second participant Cj decides not to apply the transformation P(−1) during the sub-step G3, or conversely, in the case where the first participant Ci decides not to apply the transformation P during the sub-step G2, and the second participant Cj decides to apply the transformation P(−1) during the third step G3, the information that would have circulated in the communication chain and measured by the receiver CN will not be relevant, i.e., the result of the measurement performed by the receiver CN will not be able to be exploited by the first and second participants Ci and Cj. Indeed, it will correspond to a measurement of a state of a base B0 or B1 in the corresponding incompatible base, and, as explained before, to a completely random result. In practice, this result of the transmission of the corresponding quantum bit will be withdrawn and discarded.
This is why the term “description of a quantum state qq” is used to generalise the result of the measurement done by the receiver CN because the quantum information deduced from this measurement is not necessarily relevant and does not necessarily correspond to the nature of the state qq.
Thus, depending on the decisions taken by the first and second participants Ci and Cj, information encoded in a quantum bit could be transmitted from the first participant Ci to the second participant Cj in a secure manner because the other participants, different from Ci and Cj, only have access, when the receiver CN announces the measurement of the final state, to information relating to the state |alphafinal> of the photon transmitted in the communication chain. From a statistical point of view, on average, and because of the configurations where the quantum information relating to the state |alphafinal> is random and therefore irrelevant, one out of two quantum states can be transmitted by the first participant Ci to the second participant Cj in a hidden manner from the other participants in the communication chain.
Consider herein a second case where the first participant Ci is the emitter participant C1 but the participant Cj is just a transformer, different from the receiver CN. N is then an integer greater than or equal to 3. The steps of the method for securely transmitting the sequence of quantum states may then consist in repeating the following steps, for q being an integer comprised between 1 and Q:
After the Q repetitions have been performed, the emitter C1 and the second participant Cj reconstitute, by concatenation, a sequence of the descriptions of the Q quantum states qq, discarding, where necessary, the irrelevant and non-exploitable descriptions.
Consider herein a third case where the first participant Ci is a transformer, different from the emitter C1, and the participant Cj is the receiver CN, and where N is an integer greater than or equal to 3. The steps of the method for securely transmitting the sequence of quantum states may then consist in repeating the following steps, for q being an integer comprised between 1 and Q:
After the Q repetitions have been performed, the first participant Ci and the receiver CN reconstitute, by concatenation, a sequence of the descriptions of the Q quantum states qq, discarding, where necessary, the irrelevant and non-exploitable descriptions.
A fourth and last case is considered herein where the first participant Ci is the emitter C1 and the second participant Cj is the receiver CN, and where N is an integer greater than or equal to 3. The steps of the method for securely transmitting the sequence of quantum states may then consist in repeating the following steps, for q being an integer comprised between 1 and Q:
After the Q repetitions have been performed, the emitter C1 and the receiver CN reconstitute, by concatenation, a sequence of the descriptions of the Q quantum states qq, discarding, where necessary, the irrelevant and non-exploitable descriptions.
For the previously-described second, third and fourth cases, 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.
The first and second actions carried out respectively by the first and second distinct participants Ci and Cj in the four different cases of securely transmitting sequences of quantum states will now be formally described.
Consider a Hilbert vector space encoding d-dimensional quantum states. The first action to carry out, during the q-th repetition of the succession of previously-described steps by the participant Ci may thus consist of the following steps:
and where the notation Xm designates the following transformations, respectively in the base B0 and the base B1, for m and t two integers comprised between 0 and d−1:
Xm|t>=|t+m mod d> [Math. 4]
and
Xm|et>=|et+m mod d> [Math. 5]
where the abbreviation mod stands for the mathematical function modulo.
The transformation Xm corresponds to the first step G1, and the transformation Psq corresponds to the second one G2. The effect of the first action performed by the first participant Ci, PsqXm, on a reference state |0> is illustrated in
The second action carried out, during the q-th repetition of the succession of previously-described steps by the second participant Cj may thus consist of the following steps:
The transformation P(−1)tq corresponds to the third step G3, and the transformation Xn corresponds to the fourth step G4.
Thus, in the two configurations enabling a quantum state transmission providing relevant information, i.e. either the configuration where both of the participants Ci and Cj decide during the second and third steps G2 and G3 to apply the transformations P and P(−1) respectively, i.e. the configuration where neither of the two decides during the second and third steps G2 and G3 to apply the transformations P and P(−1) respectively, the resulting encoding base at step G4 is the standard base B0. The final state |alphafinal> is equal to |m+n mod d> and could be measured in the standard base B0 by the receiver CN. The result of the measurement announced by the receiver is m+n mod d. All participants ignoring the value of m and n, i.e. all participants except the first and second participants Ci and Cj learn nothing about the value m+n mod d. The transformation Xn has the effect of masking the state transmitted by the first participant Ci when it is measured and announced by the receiver CN. Due to the disclosure of the result of the measurement by the receiver CN, m+n mod d, the participant Cj can thus deduce the state |m> transmitted to him by the participant Ci. Indeed, the transmission of the quantum state by the first participant Ci to the second participant Cj has been performed in a secure manner, because all of the other participants in the chain only know the result m+n mod d of the measurement performed by the receiver Cn.
Thus, the application of conjugate encoding through the use of incompatible encoding bases enables a secure transmission of a quantum state, or quantum information, between two first and second participants Ci and Cj, wherein the transmitted quantum state is unknown to the other participants of the communication chain.
More generally, it is possible to consider that the transmission of quantum states by the first participant Ci to the second participant Cj is repeated to transmit a plurality of messages. In this case, Ci can send a posteriori to Cj the decisions he has taken at the different repeated second steps, and Cj can select the information derived from measurements for which he has taken correct decisions during the different repeated third steps G3.
More theoretically, behind the use of conjugate encoding hides the use of the uncertainty principle of quantum physics. The use of conjugate bases has the effect that reading in one base a piece of information encoded in another base gives a completely random value. This is a maximum incompatibility, because we talk about incompatibility as soon as there is uncertainty about the sent value.
In the two other configurations that do not enable a quantum state transmission providing relevant information, i.e., as explained hereinabove, in the case where the participant Ci decides to apply the transformation P during the sub-step G2, and the participant Cj decides not to apply the transformation P(−1) during the sub-step G3, or conversely, in the case where the participant Ci decides not to apply the transformation P during the sub-step G2, and the participant Cj decides to apply the transformation P(−1) during sub-step G3, the result of the measurement announced by the receiver CN will be random and withdrawn and discarded.
According to an embodiment of the method for securely transmitting a sequence of quantum states, the dimension d of the Hilbert vector space for encoding the state vectors is equal to 2.
According to an embodiment of the invention, countermeasure mechanisms could be implemented in order to prevent third parties from being able to learn the modulations performed by the intermediate participants and thus learn the exchanged secret information.
In particular, a possible attack consists in injecting light with a given characteristic (wavelength, polarisation, and time) and measuring it after passage through an intermediate participant in order to learn its modulation characteristics.
In order to avoid this attack, filters could be implemented. To the extent that the modulators already have polarisation filtering characteristics, it is possible to simply add a frequency filter, in order to let only light pass at a predetermined frequency, and a time gate in order to let only photons pass at predetermined times (corresponding to transmissions by the emitter C1).
This strategy works by imposing constraints on the optical signals transmitted by the emitter C1.
The frequency filter could be implemented, for example, by means of a Fabry-Perot etalon, and the time gate could be an electro-optical intensity modulator, for example similar to that set up by the emitter C1.
Henceforth, the only possible attacks would consist in injecting a light with the same characteristics as those provided for by the system. This is only possible by using a beam splitter.
The use of a beam splitter would inevitably lead to a decrease in optical power. Furthermore, a splitter does not allow recovering the light injected by the adversary because it cannot be distinguished from the “legitimate” beam transmitted by the emitter. This decrease and this disturbance of the optical flux can be detected, for example, by the mechanism described below.
Another embodiment of the first case of secure transmission, where the first and second participants Ci and Cj are participants different from the participants C1 and CN, i.e. they are neither emitter nor receiver, but simply transformers and the communication chain comprises a number N of participants greater than or equal to 4, will be described, where the second and fourth steps G2 and G4 could be followed by complementary steps aimed at preventing side-channel attacks of spies on the transmission of quantum states.
During the q-th repetition of the succession of steps of the method for securely transmitting a sequence of Q quantum states qq, step G2 could be followed by the following successive steps:
Indeed, it may be considered that, since the first and second participants Ci and Cj are transformers which 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 C1 and the participant Ci polarisation photons different from those emitted by the emitter C1, which is a legitimate participant.
The light power samples sampled during the fifth and seventh steps G5 and G7 enable the measurement thereof as well as the verification of the conformity of these measurements, by the comparisons performed during the sixth and eighth steps G6 and G8, with the light power Pseq sent by the emitter C1. These samples and comparisons thus form countermeasures performed respectively by the first participant Ci and the second participant Cj.
Hence, the fifth, sixth, seventh and eighth steps G5 to G8 form additional security of the method for transmitting a sequence of quantum states between the first and second participants Ci and Cj because they allow detecting possible side-channel attacks by spies. This additional security could be implemented with simple and inexpensive hardware.
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 that one he has measured. If he has measured in an encoding base different from that one chosen by the first participant Ci, which happens half the time, then the spy will modify the photon, because of the equiprobability on the measurement results that he might get. The statistics will be modified accordingly in a visible way for the first participant Ci and the second participant Cj. By comparing a small portion of the received photons with those that have been sent, the first and second participants Ci and Cj can thus spot a spy who is listening to their conversation.
Thus, this additional security mechanism can operate independently of the frequency filter and the time gate described hereinabove, but it also allows for a synergetic effect since each of these two mechanisms targets complementary attacks and their joint use thus allows blocking a wide variety of possible attacks.
According to one embodiment, these two additional mechanisms are implemented jointly.
Preferably, the degree of freedom of the photons encoding the quantum bits is selected amongst the phase, the phase difference, the temporal location, the polarisation or the frequency of the photon.
Advantageously, the sequence of Q quantum states qq for q integer comprised 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 G2 and G3 corresponding to the “key sifting” operation performed in a standard manner in a quantum key distribution protocol.
The implementation of the method for securely transmitting a sequence of Q quantum states qq, q being an integer comprised between 1 and Q could be carried out using a device comprising:
The previously-described device could be used in the following manner. Once the first and second participants Ci and Cj have been chosen, a laser associated to the emitter C1 generates, following a command from the emitter C1, a flux of photons encoding a sequence of quantum bits. The flux of photons is transmitted in the communication chain through the initial modulator, the N−2 intermediate modulators, the final modulator, and up to the photon detector.
In the context of the transmission of a sequence of Q quantum states encoded on Q photons, for each photon:
Thus, the first participant Ci and the second participant Cj reconstitute, by concatenation, a sequence of the descriptions of the Q transmitted quantum states, discarding, where necessary, the irrelevant and non-exploitable descriptions, in the previously-described cases.
Hence, the advantage of the method for transmitting sequences of quantum states between several participants presented in this application consists in that it could be implemented by a device comprising only one laser and only one photon detector. These last components being in general the most expensive hardware elements, the protocol presented herein therefore allows carrying out a transmission of sequences of quantum states with a lower cost per participant.
In the previously-described case where the first and second participants Ci and Cj are participants other than the participants C1 and CN, the above-described device could be supplemented by:
The beam splitter Si separates the flow of photons received from the participant Ci−1 in two distinct directions, one towards the modulator of the first participant Ci then towards the rest of the communication chain, the other one towards the photodiode PDi. The second beam splitter Sj separates the flux of photons received from the participant Cj−1 in two distinct directions, one in the direction of the modulator of the second participant Cj then towards the rest of the communication chain, the other one towards the second photodiode PDj.
These additional components enable the implementation of the securing of the method for transmission of sequences of quantum states against side-channel attacks. In particular, they enable the completion of the fifth, sixth, seventh and eighth steps G5 to G8 described before. The fifth and seventh steps G5 and G7 are carried out respectively by measuring the light power Pseq1 by the photodiode PDi and by measuring the light power Pseq2. The sixth and eighth comparison steps G6 and G8 are carried out using the measurements of the light powers Pseq1 and Pseq2 and the light power prediction values Pseq1′ and Pseq2′. For example, when one of the comparisons, between Pseq1 and Pseq1′ on the one hand, and between Pseq2 and Pseq2, on the other hand, results in an inequality, an attack by a spy, for example by injection of photons, can be detected.
In this configuration, the first and second beam splitters Si and Sj are configured so that with a probability p, the photons crossing them are directed towards the first and second photodiodes PDi and PDj respectively. The photodiodes PDi and PDj can measure the average light power over a given period of time.
Thus, these additional components are also much simpler and less expensive in comparison with hardware conventionally used in quantum communication devices such as for example single photon detectors.
When the degree of freedom of the photons to encode the quantum bits is the phase, the initial modulator, the N−2 intermediate modulators and the modulator could be phase modulators. For example, the LN53S-FC or LN65S-FC model marketed by the company Thorlabs could be used.
When the degree of freedom of the photons to encode the quantum bits is the polarisation of the photons, the initial modulator, the N−2 intermediate modulators and the modulator could be polarisation modulators. For example, a model of the PSC-LN series products marketed by the company iXblue Photonics could be used.
When the degree of freedom of the photons to encode the quantum bits is the temporal location of the photons, the initial modulator, the N−2 intermediate modulators and the modulator may each comprises a number d of delay lines and a number 2d of splitter plates, where d represents the dimension of the Hilbert vector space of representation of the quantum states. The superimposition of temporal locations to be carried out to create an incompatible base could be obtained by programming the splitter plates.
Post-processing such as error correction or standard privacy amplification in quantum key distribution protocols could also be applied following the implementation of the different embodiments of the method for securely transmitting sequences of quantum states.
According to some embodiments, the invention may have several advantages:
According to embodiments of the invention, it is possible to connect different devices, in order to form transmission networks on a larger scale.
Thus, each device as previously described could allow covering a geographical area with a moderate size, corresponding for example to an urban or metropolitan area (of the MAN type, standing for “Metropolitan Area Network”). These networks could be connected together on a national or international scale at interconnection points whose functions are to transmit keys from one network to another. These network interconnections could for example be done through satellite networks, allowing interconnecting the metropolitan networks.
Number | Date | Country | Kind |
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1909839 | Sep 2019 | FR | national |
Filing Document | Filing Date | Country | Kind |
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PCT/EP2020/074576 | 9/3/2020 | WO |
Publishing Document | Publishing Date | Country | Kind |
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WO2021/043891 | 3/11/2021 | WO | A |
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Number | Date | Country | |
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20220311604 A1 | Sep 2022 | US |