Quantum signal encoding method and quantum key extraction method suitable for quantum key distribution

Abstract

The application discloses a quantum signal encoding method and a quantum key extraction method suitable for quantum key distribution, wherein the quantum key extraction method comprises the following steps: using a polarizing plate and a polarizing beam splitter to randomly select a horizontal, vertical, positive 45-degree or negative 45-degree base vector to project and measure the polarization state of an encoded optical pulse signal sent by a sending terminal; randomly inputting the projection measurement result into a first detector or a second detector with asymmetric performance parameters to obtain a measurement result; reserving the measurement result of the measurement base vector consistent with the base vector disclosed by the sending terminal; estimating channel parameters by using a decoy state, and calculating the size of a key rate by using the estimated channel parameters; and extracting a final key from the reserved measurement result according to the size of the key rate. The application can improve the key coding rate and improve the practicability of the quantum key distribution system.

Description

TECHNICAL FIELD

[0001] The present application relates to a quantum signal encoding method, a quantum key extraction method, an electronic terminal and a storage medium suitable for quantum key distribution, and belongs to the technical field of information security. BACKGROUND

[0002] With the continuous updating of decoding algorithms and the rapid development of computer technology, the time to crack the password system will be shorter and shorter, that is, the security of the traditional password system will be lower and lower over time. In view of this situation, some researchers combine cryptography and quantum mechanics and propose a new generation of password system-quantum password system, the core of which is quantum key distribution (QKD), and its security no longer depends on the complexity of mathematical problems, but on the principles of quantum physics, which has absolute security in theory.

[0003] Quantum key distribution has developed into a mature science over the past 30 years and is gradually moving from theoretical analysis and laboratory testing to engineering experiments. Among all the development directions in the field of quantum information, quantum key distribution is the first to enter life from the laboratory, and it is another great contribution of physics to human life. In these processes, the BB84 protocol is the earliest and most simple and practical scheme. The decoy state technology proposed later effectively resists photon number splitting attacks, greatly improving the security and transmission distance of the BB84 protocol. In the system of the BB84 protocol, the receiving end usually uses two detectors to generate bits 0 and 1. In the past model, it is usually assumed that the two detectors have symmetric performance parameters, that is, the detection efficiency and dark count of the two detectors are the same. However, in reality, it is difficult to have two detectors with exactly the same parameters, because it is not easy to manufacture two detectors with exactly the same parameters. The usual practice is to compromise the parameters of the two detectors according to the worst case, so as to meet the requirements of the model. However, this cannot reflect the true performance of the system, for example, it will reduce the code rate of the system and reduce the transmission distance of the key. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art and provide a quantum signal encoding method, a quantum key extraction method, an electronic terminal and a storage medium suitable for quantum key distribution, which can improve the key code rate.

[0005] To achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0006] In a first aspect, the present application provides a quantum signal encoding method suitable for quantum key distribution, which is executed by a sending terminal and includes:

[0007] The generated continuous light pulse signal is randomly modulated to generate signal state, decoy state and vacuum state required for quantum key distribution, and the signal intensity of the signal state, decoy state and vacuum state is μ, v and o respectively, and μ>v>o;

[0008] The randomly modulated light pulse signal is randomly prepared as one of the four encoding states of the BB84 protocol, and is sent to the receiving terminal; wherein the four encoding states include horizontal polarization state, vertical polarization state, positive 45° polarization state and negative 45° polarization state.

[0009] In combination with the first aspect, further, the photon number probability distribution of the generated light pulse signal is set as:

[0010]

[0011] Wherein, n is the number of photons in the light pulse, n∈{0,1,2,...}; λ is the light pulse intensity, λ∈{μ,v}; e is the natural base.

[0012] Secondly, the present application provides a quantum signal encoding method based on any one of the first aspect, which is executed by a receiving terminal and includes:

[0013] Randomly selecting horizontal, vertical, positive 45° or negative 45° base vector to project and measure the polarization state of the encoded light pulse signal sent by the sending terminal;

[0014] Randomly inputting the projection measurement result into the first detector or the second detector with asymmetric performance parameters to obtain the measurement result; the performance parameters include penetration efficiency and dark count;

[0015] Reserving the measurement result of the measurement base vector consistent with the base vector announced by the sending terminal, and obtaining the single photon counting rate and the single photon error rate according to the reserved measurement result;

[0016] Estimating the channel parameters by using the decoy state, and calculating the key rate size by using the estimated channel parameters; wherein the channel parameters include the lower bound of the single photon counting rate and the upper bound of the single photon error rate;

[0017] Extracting the final key from the reserved measurement result according to the key rate size.

[0018] In combination with the second aspect, further, before calculating the key rate size, the gain and the average error rate of the receiving terminal are calculated, including:

[0019] The gain of the receiving terminal receiving the encoding bit 0 when the sending terminal sends the encoding bit 0 is calculated as:

[0020] ​

[0021] The sending terminal sends the encoding bit 0, and the receiving terminal receives the gain of the encoding bit 1

[0022] The sending terminal sends the encoding bit 1, and the receiving terminal receives the gain of the encoding bit 0

[0023]

[0024] The sending terminal sends the encoding bit 1, and the receiving terminal receives the gain of the encoding bit 1

[0025]

[0026]

[0027] Wherein, e d is the background error, η0 and η1 represent the total penetration efficiency of the first detector and the second detector respectively: η t represents the penetration efficiency of the channel; n represents the number of photons in the optical pulse signal; d0 and d1 represent the dark count of the first detector and the second detector respectively; represents the probability distribution of the number of photons of the optical pulse signal generated by excitation;

[0028] The total gain Q of the receiving terminal is calculated λ And the total error rate T λ :

[0029]

[0030]

[0031] The average error rate E is calculated according to the total gain and the total error rate of the receiving terminal λ E λ = T λ / Q λ .

[0032] In combination with the second aspect, further, the calculation formula of the key rate size is as follows:

[0033]

[0034] Wherein, R is the key rate size;

[0035] Y1 L is the lower bound of single photon counting rate,

[0036] ​​​ P0 is the distribution probability of 0 photons in the signal state,

[0037] P0 is the distribution probability of 0 photons in the signal state, μ P1 is the distribution probability of 1 photon in the signal state, P2 is the distribution probability of 2 photons in the signal state, P0 is the distribution probability of 0 photons in the signal state, ν P1 is the distribution probability of 1 photon in the signal state, P2 is the distribution probability of 2 photons in the signal state, P0 is the distribution probability of the vacuum state; Y0 is the channel transmittance of the vacuum state; e0 is the error rate of the vacuum state; q is the efficiency of the basis, Q μ Q is the total gain of the receiving terminal corresponding to the signal state; v T is the total gain of the receiving terminal corresponding to the decoy state; v E is the total error rate corresponding to the decoy state; μ f is the efficiency coefficient of error correction, and H2() is a binary entropy function.

[0038] The third aspect of the present application provides an electronic terminal, comprising a processor and a memory connected with the processor, and the memory stores a computer program, when the computer program is executed by the processor, the steps of the method of any preceding aspect are executed.

[0039] The fourth aspect of the present application provides a computer readable storage medium, which stores a computer program, and the program is executed by the processor to realize the steps of the method of any preceding aspect.

[0040] Compared with the prior art, the present application has the following beneficial effects:

[0041] The present application regards the performance of two detectors of the receiving terminal as two independent parameters instead of the same parameter, calculates the gain reaching each detector, estimates the channel parameter by the decoy state method, strictly calculates the size of the key rate, and finally extracts the final key string from the measurement result by using the size of the key rate, which greatly improves the practicability and code rate of the decoy state quantum key distribution method. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 FIG. 1 is a structural schematic diagram of a quantum key distribution system provided by an embodiment of the present application;

[0043] Figure 2 FIG. 2 is the influence of different dark count rates of the second detector on the key rate in the embodiment of the present application;

[0044] Figure 3is the influence of different detection rates of the second detector on the key rate in the embodiment of the application. DETAILED DESCRIPTION

[0045] The technical solutions of the application will be described in detail below with reference to the drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solutions of the application, rather than limitations of the technical solutions of the application. In the case of no conflict, the technical features in the embodiments and the embodiments can be combined with each other.

[0046] As Figure 1 shown, it is a structure schematic diagram of a quantum key distribution system provided by an embodiment of the application, comprising a sending terminal Alice and a receiving terminal Bob. The sending terminal Alice comprises a light source, an intensity modulator IM and a first polarizing wave plate PR, wherein the light source is used to generate a light pulse signal with a certain photon number distribution, the intensity modulator IM is used to modulate the light pulse signal into different intensities, and the first polarizing wave plate PR is used to prepare the light pulse signal with different intensities into different encoding state signals. The receiving terminal Bob comprises a second polarizing wave plate PR, a polarizing beam splitter PBS, a first detector D0 and a second detector D1, the second polarizing wave plate PR and the polarizing beam splitter PBS are used to select base vectors to project and measure the polarized state signals sent by the sending terminal, and the first detector D0 and the second detector D1 are used to generate bits 0 and 1.

[0047] Embodiment one:

[0048] The embodiment of the application provides a quantum signal encoding method suitable for quantum key distribution, which can be executed by a sending terminal as shown in Figure 1 , and comprises the following steps.

[0049] Step one: generating continuous light pulse signals;

[0050] Referring to Figure 1 , the light pulse signals can be generated by a light source in the sending terminal, and the photon number probability distribution of the generated light pulse signals can be set as:

[0051]

[0052] wherein n is the number of photons in the light pulse, n∈{0,1,2,...}; λ is the intensity of the light pulse, i.e. the average number of photons, λ∈{μ,v}; and e is the natural base.

[0053] Step two: randomly modulating the light pulse signals to generate signal states, decoy states and vacuum states required for quantum key distribution;

[0054] In the embodiment of the present application, the intensity modulator IM is used to randomly modulate the optical pulse signal to generate three intensity optical pulse signals represented by {μ,ν,ο}, which are used as signal state, decoy state and vacuum state respectively, wherein μ>ν>ο;

[0055] Step three: the randomly modulated optical pulse signal is randomly prepared as one of the four encoding states of the BB84 protocol and is sent to the receiving terminal;

[0056] The four encoding states include horizontal polarization state, vertical polarization state, positive 45° polarization state and negative 45° polarization state.

[0057] The method provided in the embodiment can be applied to a terminal, for example, any smart phone, tablet computer or computer device with communication function, and can be realized by software and / or hardware.

[0058] Embodiment two:

[0059] The quantum key extraction method provided in the embodiment can be executed by the receiving terminal as shown in the figure, and includes the following steps. Figure 1

[0060] Step one: randomly select horizontal, vertical, positive 45° or negative 45° base vectors to project and measure the polarization state of the encoded optical pulse signal sent by the sending terminal;

[0061] The selection of the base vectors can be realized by the second polarization wave plate PR and the polarization beam splitter PBS of the receiving terminal.

[0062] Step two: randomly input the projection measurement result into the first detector or the second detector with asymmetric performance parameters to obtain a measurement result; the performance parameters include penetration efficiency and dark count;

[0063] The successful measurement result is the response of the first detector D0 or the second detector D1, which generates bits 0 and 1;

[0064] Step three: retain the measurement result of the measurement base vector consistent with the base vector announced by the sending terminal, and obtain the single photon counting rate and the single photon error rate according to the retained measurement result;

[0065] Step four: estimate the channel parameters by using the decoy state, and calculate the key rate size by using the estimated channel parameters; wherein the channel parameters include the lower bound of the single photon counting rate and the upper bound of the single photon error rate;

[0066] The performance parameters of the two detectors of the receiving terminal Bob are asymmetric, that is, the total detection efficiency and dark count of the first detector D0 and the second detector D1 are two independent sets of parameters, and it is assumed that the total detection efficiency and dark count of the first detector D0 are ​and d0, the total detection efficiency and dark count of the second detector D1 are and d1,

[0067] When considering the dark count, the encoding bit 0 is sent, after passing through the beam splitter, k photons go to the first detector D0, and the detection is the encoding bit 0, there are two cases,

[0068] (1) When k>0, the probability of the first detector D0 responding and the second detector D1 not responding is (1-d1);

[0069] (2) When k=0, the probability of the first detector D0 responding and the second detector D1 not responding is d0(1-d1).

[0070] Therefore, the dark count response model for the first detector D0 is:

[0071]

[0072] Similarly, the dark count response model for the second detector D1 is:

[0073]

[0074] After the measurement is completed, the sending terminal Alice publishes the intensity λ and the base vector prepared for each light pulse, and the receiving terminal Bob publishes the measured base vector, and retains the measurement result of the same base vector; then the gain of the receiving terminal receiving the encoding bit 0 when the sending terminal sends the encoding bit 0 is:

[0075]

[0076] wherein is the probability distribution of the number of photons of the light source, is the probability of the photons going to the detector D0 (correct detection). represents the probability of the transmitted n-photon state decaying to k photons at the receiving terminal, wherein is a binomial distribution, which can be further simplified as:

[0077]

[0078] wherein, e d is the background error, which represents the probability of the detector responding incorrectly (for example, the receiving terminal judges the encoding bit 1 when the encoding bit 0 is sent);

[0079] Similarly, the gain of the receiving terminal receiving the encoding bit 1 when the sending terminal sends the encoding bit 0 is:

[0080]

[0081] The gain of the receiving terminal receiving the encoding bit 0 when the sending terminal sends the encoding bit 1 is:

[0082]

[0083] The sending terminal sends the encoded bit 1, and the receiving terminal receives the gain for the encoded bit 1 as:

[0084]

[0085] where η0and η1represent the total transmission efficiency of reaching the detectors D0and D1, respectively: η t represents the transmission efficiency of the channel.

[0086] The total gain Q of the receiving terminal is calculated as: λ and the total bit error rate T is calculated as: λ

[0087]

[0088]

[0089] The average bit error rate E is calculated as: λ E = T / Q λ λ λ

[0090] The channel parameters in the decoy state estimation scheme, i.e., the lower bound of the single-photon counting rate and the upper bound of the single-photon bit error rate, are:

[0091]

[0092]

[0093] Using the channel parameters, the final key rate R of the scheme can be calculated as

[0094]

[0095] where P0 is the distribution probability of 0 photons in the signal state; P1 μ is the distribution probability of single photons in the signal state; is the distribution probability of double photons in the signal state; is the distribution probability of 0 photons in the decoy state; P1 ν is the distribution probability of single photons in the decoy state; is the distribution probability of double photons in the decoy state; P0is the distribution probability of the vacuum state (i.e., 0 photons); Y0is the channel transmission rate of the vacuum state (i.e., 0 photons); e0is the bit error rate of the vacuum state (i.e., 0 photons); q is the efficiency of the basis, Q μ is the total gain of the receiving terminal corresponding to the signal state; Q v ​​​​Total gain of receiving terminal corresponding to decoy state; T v Total error rate corresponding to decoy state; E μ Average error rate corresponding to signal state, which can be calculated according to the calculation formula of E λ , and λ = μ; f is an error correction efficiency coefficient, and H2() is a binary entropy function.

[0096] Step five: extracting a final key from the reserved measurement results according to the key rate size.

[0097] The Figure 2 Firstly, a diagram of the relationship between the key rate R and the transmission distance is shown when the detection efficiency and is equal to 0.5, e d is 0.03, d0 is 10 -6 , and d1 is 10 -4 , 10 -5 , 10 -6 , 10 -7 , 10 -8 respectively. From the diagram, it can be seen that the greater the value of d1 is, the faster the transmission distance of the key decreases, and the key rate at a short distance is almost consistent. This shows that the dark count rate mainly affects the transmission distance, and when we want to perform long-distance key distribution, the dark count rate of the detector should be reduced.

[0098] The Figure 3 A diagram of the relationship between the key rate R and the transmission distance is shown when d0 = d1 = 10 -6 , e d = 0.03, is 0.1, 0.3, 0.5, 0.7, 0.9 respectively. From the diagram, it can be seen that as the value of e increases, the key generation rate at each distance increases, but the transmission distance of the key is less affected.

[0099] In summary, the method provided by the embodiment of the application regards the performances of two detectors of a receiving terminal in a quantum key distribution system as independent parameters instead of the same parameter, and establishes a more universal mathematical model of decoy state quantum key distribution on this basis, thereby greatly improving the practicability of the decoy state quantum key distribution method.

[0100] Embodiment three

[0101] The embodiment of the application further provides an electronic terminal, including a processor and a storage medium.

[0102] The storage medium is used for storing instructions.

[0103] The processor is configured to operate according to the instructions to perform the steps of the method of embodiment one or embodiment two.

[0104] The electronic terminal provided by the embodiments of the present application can execute the method provided by any of the embodiments of the present application, and has the corresponding function modules and beneficial effects of the execution method.

[0105] Embodiment four:

[0106] The embodiments of the present application also provide a computer readable storage medium, which stores a computer program, and the program is executed by a processor to perform the steps of the method of embodiment one or embodiment two.

[0107] The storage medium provided by the embodiments of the present application can execute the method provided by any of the embodiments of the present application, and has the corresponding function modules and beneficial effects of the execution method.

[0108] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) containing computer-usable program code.

[0109] The present application is described with reference to flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus produce a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in one or more flows and / or blocks Figure 1 The functions specified in one or more flows and / or blocks

[0110] These computer program instructions can also be stored in a computer readable memory that can direct the computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer readable memory produce a manufactured product including instruction devices that implement the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in one or more flows and / or blocks Figure 1 The functions specified in one or more flows and / or blocks

[0111] These computer program instructions can also be loaded into a computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable data processing devices to generate a computer implemented process, so that the instructions executed on the computer or other programmable data processing devices provide a process for implementing the functions specified in the flowchart Figure 1 or multiple flows and / or blocks Figure 1 of the flowchart or multiple flows and / or blocks of the block diagram. The above descriptions are only the preferred embodiments of the present application, and it should be pointed out that, for those skilled in the art, without departing from the technical principles of the present application, a number of improvements and modifications can be made, and these improvements and modifications should also be considered as the protection scope of the present application.

Claims

1. A quantum key extraction method executed by a receiving terminal, characterized by, The quantum signal is encoded by the transmitting terminal through the following encoding method: a continuous optical pulse signal is generated by excitation, and the optical pulse signal is randomly modulated to generate signal states, decoy states and vacuum states required for quantum key distribution, the signal strengths of the signal states, decoy states and vacuum states are μ, v and o respectively, and μ>v>o; the randomly modulated optical pulse signal is randomly prepared into one of four encoding states of the BB84 protocol, and is sent to the receiving terminal; wherein the four encoding states include horizontal polarization state, vertical polarization state, positive 45° polarization state and negative 45° polarization state; The extraction method comprises: Randomly selecting horizontal, vertical, positive 45° or negative 45° base vectors to project and measure the polarization state of the encoded optical pulse signal sent by the transmitting terminal; The projection measurement result is randomly input to the first detector or the second detector with asymmetric performance parameters to obtain a measurement result; the performance parameters include penetration efficiency and dark count; The measurement result of the measurement base vector consistent with the base vector announced by the transmitting terminal is reserved, and the single-photon count rate and the single-photon error rate are obtained according to the reserved measurement result; Channel parameters are estimated using decoy states, and the size of the key rate is calculated using the estimated channel parameters; wherein the channel parameters include the lower bound of the single-photon count rate and the upper bound of the single-photon error rate; The final key is extracted from the reserved measurement result according to the size of the key rate; Before calculating the size of the key rate, the gain and the average error rate of the receiving terminal are calculated, including: The transmitting terminal calculates the transmitting code bit 0, and the receiving terminal receives the gain of the code bit 0 is: ， The transmitting terminal calculates the gain for transmitting the encoded bit 0, and the receiving terminal receives the gain for receiving the encoded bit 1 is: ， The transmitting terminal calculates the gain for transmitting the encoded bit 1, and the receiving terminal receives the gain for the encoded bit 0 is: ， The transmitting terminal calculates the transmitting code bit 1, and the receiving terminal receives the gain of the code bit 1 is: ， wherein, is the background error rate, and represent the total transmission efficiency to the first and second detectors, respectively: , , represents the transmission efficiency of the channel; n represents the number of photons in the optical pulse signal; d0 and d1 represent the dark counts of the first and second detectors, respectively; represents the probability distribution of the number of photons of the optical pulse signal generated by excitation; Computing the total gain of the receiving terminal and the total bit error rate : ， ， calculating an average bit error rate from the total gain of the receiving terminal and the total bit error rate to be: ; The calculation formula of the size of the key rate is as follows: ， Wherein, R is the size of the key rate; is a lower bound for the single-photon count rate, ; is an upper bound for the single photon error rate, ; is the distribution probability of 0 photons in the signal state; is the distribution probability of single photons in the signal state; is the distribution probability of double photons in the signal state; is the distribution probability of 0 photons in the decoy state; is the distribution probability of single photons in the decoy state; is the distribution probability of double photons in the decoy state; P0 is the distribution probability of the vacuum state; Y0 is the channel transmission rate of the vacuum state; e0 is the bit error rate of the vacuum state; is the efficiency of the reference; is the total gain of the receiving terminal corresponding to the signal state; is the total gain of the receiving terminal corresponding to the decoy state; is the total bit error rate corresponding to the decoy state; is the average bit error rate corresponding to the signal state; is the correction efficiency coefficient, is a binary entropy function.

2. The quantum key extraction method according to claim 1, wherein, The photon number probability distribution of the generated optical pulse signal is set as: ， wherein n represents the number of photons in the optical pulse signal; ; is the optical pulse intensity, ∈{μ, v}; e is the natural base.

3. An electronic terminal, characterized in that The processor and the memory connected to the processor are included, and the computer program is stored in the memory, when the computer program is executed by the processor, the steps of the method of claim 1 or 2 are executed.

4. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to realize the steps of the method of claim 1 or 2.

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