A Dual-Field Quantum Key Distribution Method Based on a Discrete-Phase Randomized Light Source
By using discrete phase randomization light sources in dual-field quantum key distribution, the problem of difficulty in achieving continuous phase randomization light sources is solved, the key rate is improved and the rate-loss boundary is broken, and higher security and efficiency are achieved.
Patent Information
- Application Number
- CN202310006809.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-01-04
- Publication Date
- 2025-07-11
- Estimated Expiration
- 2043-01-04
AI Technical Summary
In the prior art, it is difficult to achieve using a coherent state light source with continuous phase randomization, resulting in a reduced security of the actual TF-QKD protocol and a reduced key rate within the low channel loss range.
A two-field quantum key distribution method based on discrete phase randomization light source is adopted. The final security key is obtained by randomly selecting the phase of the coherent state in the encoding mode and the test mode, and using a detector for measurement and information disclosure, combining error correction and confidential amplification.
The key rate is improved within the low channel loss range and the phase filtering factor 2/M is not required, breaking the rate-loss boundary and achieving higher security and efficiency.
Smart Images
Figure CN116232575B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a two-field quantum key distribution method based on a discrete-phase randomized light source, belonging to the field of quantum information technology. Background Art
[0002] Quantum key distribution (QKD) is a communication method based on quantum mechanics that can provide unconditionally secure keys for two communicating parties, Alice and Bob, even in the presence of eavesdroppers. Since the first QKD protocol was proposed in 1984, a large number of theoretical and experimental studies have been conducted in this field, and a series of new protocols have been proposed to improve and enhance the security and transmission distance of QKD systems. However, none of these protocols have broken the rate-loss bound, resulting in a limitation on the transmission distance of QKD protocols. Fortunately, M. Lucamarini et al. proposed a two-field quantum key distribution (TF-QKD) protocol in 2018, which breaks the rate-loss bound and increases the transmission distance. Since the TF-QKD protocol was proposed, many variant protocols have also been proposed, further improving the security of the original TF-QKD protocol. In some variant protocols, in order to ensure the security of the protocol, the quantum state needs to be randomly switched between the encoding mode and the test mode. Generally, the decoy state method is used in the test mode to estimate the information of eavesdroppers. However, in traditional decoy state protocols, it is usually assumed that a continuous-phase randomized coherent state light source is used, which is difficult to achieve in practice and reduces the security of practical TF-QKD protocols. At the same time, some previous variant protocols require phase post-selection in the encoding mode, and within the range of low channel loss, the phase screening condition will reduce the key rate. Summary of the Invention
[0003] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a two-field quantum key distribution method based on a discrete-phase randomized light source, so as to solve the problems that it is difficult to use a continuous randomized-phase coherent state light source in practical technologies and the phase screening condition will reduce the key rate.
[0004] To achieve the above object, the present invention is implemented by the following technical solutions:
[0005] In a first aspect, the present invention provides a two-field quantum key distribution method based on a discrete-phase randomized light source, including three participating parties: the communicating parties Alice and Bob, and an untrusted third party Eve. Alice and Bob select an encoding mode or a test mode in each round of communication. If the encoding mode is selected, Alice and Bob encode the classical bits 0 and 1 on the 0 and π phases of the coherent state respectively. If the test mode is selected, Alice and Bob modulate the coherent state phase with a random number 0, π / M, 2π / M,..., (M - 1)π / M, where M represents the number of phases modulated by Alice and Bob. When there is a subsequent selection of phases in the test mode, the method includes:
[0006] Step 1: Alice and Bob select an encoding mode or a test mode in each round of communication, and in the encoding mode, randomly generate a key bit b A (b B ), and prepare a first coherent state. In the test mode, randomly select an intensity ξ a (ξ b ) and a random number x(y) to prepare a second coherent state;
[0007] Step 2: Alice and Bob send the prepared first coherent state and second coherent state to the untrusted third party Eve. Eve uses two preset detectors L or R for measurement, announces the measurement results, and obtains successful measurement events according to the measurement results;
[0008] Step 3: Repeat the above steps. For successful measurement events, Alice and Bob announce the corresponding modes they selected. If both are in the encoding mode, take b A (b B ) as the raw key. If both are in the test mode, Alice and Bob respectively announce ξ a , ξ b , x and y. Both parties only save the bit information where ξ a = ξ b and x = y or x = y ± M / 2, and calculate the gain;
[0009] Step 4: Alice and Bob perform error correction and privacy amplification according to the calculated gain to obtain the final secure key.
[0010] Further, the first coherent state is
[0011] Further, the second coherent state is where x, y ∈ {0, 1, 2,..., M - 1}, ξ a , ξ b∈ {μ, ν, ω}, where M represents the number of modulation phases of Alice and Bob.
[0012] Furthermore, the measurement results include: only detector L responds, only detector R responds, or no detector responds. If both detectors respond, it is regarded as no detector responding.
[0013] Furthermore, the successful measurement events include: only detector L responds or only detector R responds, which are regarded as successful measurement events.
[0014] Furthermore, in step 3, if only detector R responds, Bob needs to invert his key bit b B .
[0015] Furthermore, the formula for the final secure key is:
[0016]
[0017] where H(x) = -x log2 x - (1 - x) log2(1 - x) is the binary Shannon entropy, f represents the efficiency of the error correction protocol, Q μ and e μ represent the total gain and total bit error rate when the quantum state intensity is μ in the coding mode, and represents Eve's Holevo information.
[0018] In a second aspect, the present invention provides a two-field quantum key distribution method based on a discrete phase randomized light source, including three participating parties: the communicating parties Alice and Bob, and an untrusted third party Eve. Alice and Bob select a coding mode or a test mode in each round of communication. If the coding mode is selected, Alice and Bob encode the classical bits 0 and 1 on the 0 and π phases of the coherent state respectively; if the test mode is selected, Alice and Bob modulate the phase of the coherent state with a random number 0, π / M, 2π / M,..., (M - 1)π / M, where M represents the number of modulation phases of Alice and Bob. When there is no post-selection of phases in the test mode, the method includes:
[0019] Step 1: Alice and Bob select a coding mode or a test mode in each round of communication, and in the coding mode, randomly generate a key bit b A (b B ), and prepare the first coherent state. In the test mode, randomly select an intensity ξ a (ξ b ) and a random number x(y) to prepare the second coherent state;
[0020] Step 2: Alice and Bob send the prepared first coherent state and second coherent state to the untrusted third party Eve. Eve uses two preset detectors L or R for measurement and announces the measurement results, where the measurement results include only detector L responding, only detector R responding, or no detector responding; for the encoding mode, both detectors responding is regarded as no detector responding; for the test mode, both detectors responding is regarded as randomly one of detector L or detector R responding; among them, only detector L responding or only detector R responding is regarded as a successful measurement event;
[0021] Step 3: Repeat the above steps. For successful measurement events, Alice and Bob announce the corresponding modes they choose. If they are both in the encoding mode, take b A (b B ) as the raw key. At the same time, if only detector R responds, Bob needs to invert his key bit b B . If they are both in the test mode, if they are both in the test mode, Alice and Bob respectively announce ξ a , ξ b values to calculate the gain;
[0022] Step 4: Alice and Bob perform error correction and privacy amplification according to the calculated gain to obtain the final secure key.
[0023] Furthermore, the first coherent state is
[0024] The second coherent state is where x, y ∈ {0, 1, 2,..., M - 1}, ξ a , ξ b ∈ {μ, ν, ω}, and M represents the number of modulation phases of Alice and Bob.
[0025] Furthermore, the formula for the final secure key is:
[0026]
[0027] where H(x) = -x log2x - (1 - x) log2(1 - x) is the binary Shannon entropy, f represents the efficiency of the error correction protocol, Q μ and e μ represent the total gain and total bit error rate when the quantum state intensity is μ in the encoding mode, represents Eve's Holevo information.
[0028] Compared with the prior art, the beneficial effects achieved by the present invention:
[0029] The present invention provides a dual-field quantum key distribution method based on a discrete-phase randomized light source. By using a discrete-phase randomized light source to bridge the gap between theory and practice, the rate-loss bound can be broken under the condition of only a small number of discrete phases. At the same time, the phase post-selection step means that more information is transmitted in the classical post-processing stage and more keys are consumed in the authentication of classical information. Compared with the protocol that requires a phase post-selection step in the coding mode, the present invention does not require a phase screening factor of 2 / M in the security key formula. Therefore, this method will obtain a higher key rate in the range of low channel loss. Brief Description of the Drawings
[0030] Figure 1 is a schematic diagram of the principle of a dual-field quantum key distribution method based on a discrete-phase randomized light source provided by an embodiment of the present invention;
[0031] Figure 2 is a schematic diagram of the performance simulation of Protocol 1 in an embodiment of the present invention;
[0032] Figure 3 is a performance simulation comparison diagram between Protocol 1 in an embodiment of the present invention and [1] Physical Review Applied 14, 064070 (2020);
[0033] Figure 4 is a schematic diagram of the performance simulation of Protocol 2 in an embodiment of the present invention;
[0034] Figure 5 is a performance simulation comparison diagram between Protocol 2 in an embodiment of the present invention and [2] Quantum Information Processing 20, 199 (2021). Detailed Embodiment
[0035] The present invention will be further described below with reference to the drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention and cannot be used to limit the protection scope of the present invention.
[0036] Embodiment 1
[0037] As Figure 1As shown in the figure, this embodiment introduces a dual-field quantum key distribution method based on a discrete-phase randomized light source, including: three participants, namely the communicating parties Alice and Bob and the untrusted third party Eve. In each round of communication, Alice and Bob choose an encoding mode or a test mode. If they choose the encoding mode, Alice and Bob encode the classical bits 0 and 1 on the 0 and π phases of the coherent state respectively. If they choose the test mode, Alice and Bob modulate the coherent state phase with a random number 0, π / M, 2π / M,..., (M - 1)π / M, where M represents the number of phases modulated by Alice and Bob. According to whether there is a phase post-selection in the test mode, we will propose two schemes, named Protocol 1 and Protocol 2 respectively. We first consider the case of phase post-selection in the test mode. The specific steps of Protocol 1 are as follows:
[0038] Step 1: In each round of communication, Alice and Bob choose an encoding mode or a test mode. If they choose the encoding mode, Alice and Bob randomly generate a key bit b A (b B ), and prepare a coherent state If they choose the test mode, Alice and Bob randomly select an intensity ξ a (ξ b ) and a random number x(y) to prepare a coherent state where x, y ∈ {0, 1, 2,..., M - 1}, ξ a , ξ b ∈ {μ, ν, ω}, and M represents the number of phases modulated by Alice and Bob.
[0039] Step 2: Alice and Bob send the prepared states to the untrusted third party Eve. Eve uses two detectors L or R for measurement and announces the measurement results. The available measurement results include only detector L responding, only detector R responding, or no detector responding. If both detectors respond, it is regarded as no detector responding. Among them, only detector L responding or only detector R responding is regarded as a successful measurement event.
[0040] Step 3: Repeat the above steps multiple times. For successful measurement events, Alice and Bob announce the corresponding modes they choose. If they are both in the encoding mode, take b A (b B ) as the raw key. At the same time, if only detector R responds, Bob needs to invert his key bit b B . If they are both in the test mode, Alice and Bob respectively announce ξ a , ξ b , x and y. Both parties only keep ξ a = ξb and the bit information of x = y or x = y ± M / 2, and calculate the gain.
[0041] Step 4: Alice and Bob perform error correction and privacy amplification to obtain the final secure key.
[0042] The formula for the final secure key rate is:
[0043]
[0044] where H(x) = -x log2 x - (1 - x) log2(1 - x) is the binary Shannon entropy, f represents the efficiency of the error correction protocol, Q μ and e μ represent the total gain and total bit error rate when the quantum state strength is μ in the coding mode, represents Eve's Holevo information.
[0045] Embodiment 2
[0046] Based on Embodiment 1, in order to simplify the implementation conditions of the actual system, we can further remove the post-selection step of the phase of the test mode, that is, Protocol 2, and its specific steps are as follows:
[0047] Step 1: Alice and Bob select the coding mode or the test mode in each round of communication. If the coding mode is selected, Alice and Bob randomly generate a key bit b A (b B ), and prepare a coherent state If the test mode is selected, Alice and Bob randomly select an intensity ξ a (ξ b ) and a random number x(y) to prepare a coherent state where x, y ∈ {0, 1, 2,..., M - 1}, ξ a , ξ b ∈ {μ, ν, ω}, and M represents the number of modulation phases of Alice and Bob.
[0048] Step 2: Alice and Bob send the prepared states to the untrusted third party Eve, and Eve uses two detectors L or R for measurement and announces the measurement results. The available measurement results include only the detector L responding, only the detector R responding, or no detector responding. For the coding mode, both detectors responding is regarded as no detector responding. For the test mode, both detectors responding is regarded as randomly one of the detector L or the detector R responding. Among them, only the detector L responding or only the detector R responding is regarded as a successful measurement event.
[0049] Step 3: Repeat the above steps multiple times. For successful measurement events, Alice and Bob announce the corresponding modes they have chosen. If they are both in the encoding mode, use b A (b B ) as the raw key. Meanwhile, if only detector R responds, Bob needs to invert his key bit b B . If they are both in the test mode, Alice and Bob respectively announce the values of ξ a , ξ b to calculate the gain.
[0050] Step 4: Alice and Bob perform error correction and privacy amplification to obtain the final secure key.
[0051] The formula for the final secure key rate is:
[0052]
[0053] where H(x) = -x log2 x - (1 - x) log2(1 - x) is the binary Shannon entropy, f represents the efficiency of the error correction protocol, Q μ and e μ represent the total gain and total bit error rate when the quantum state strength is μ in the encoding mode, represents Eve's Holevo information.
[0054] Example 3
[0055] As Figure 1 shown, for a typical TF-QKD system, we assume that the detection efficiency and dark count rate of the single-photon detector are 20% and 10 -8 respectively, the negotiation efficiency is 1.1, and the calibration error is 1.5%. The security analysis of Protocol 1 and Protocol 2 will be specifically introduced below.
[0056] For Protocol 1, when Alice and Bob both choose the test mode, and ξ a = ξ b = ξ, x = y, the joint quantum state ρ AB of Alice and Bob can be expressed as
[0057]
[0058] where, represents the probability of obtaining an approximate k-photon number state under the phase matching condition. When ξ a = ξ b = ξ and , the joint quantum state ρ AB of Alice and Bob can be expressed as
[0059]
[0060] wherein, represents the probability of obtaining an approximate k - photon number state under the condition of opposite phases. of.
[0061] Eve's collective attack can be described as
[0062]
[0063] where U represents any unitary operation of Eve; |e> E represents Eve's auxiliary system; or represents any quantum state corresponding to different measurement results |L>, |R> or |N> announced by Eve. represents the counting rate under different measurement results, satisfying and for different intensities ξ a and ξ b , Y k ξ satisfies where
[0064] When Alice and Bob simultaneously select encoding modes, their quantum states can be expressed in the following four forms:
[0065]
[0066]
[0067]
[0068]
[0069] Here we define and for further simplifying the formula, we define: and
[0070] We first consider the case where the measurement result is |L>. At this time, Eve's quantum state can be expressed as
[0071]
[0072] where P{|x>} = |x><x|.
[0073] Therefore, when Eve's measurement result is L, the gain of the system is
[0074]
[0075] And the corresponding bit error rate is
[0076]
[0077] According to the strong subadditivity of von Neumann entropy and Jensen's inequality, when L responds, the upper bound of Eve's Holevo information is
[0078]
[0079] Therefore, for the case where Eve announces the measurement result as |L>, the key rate formula is
[0080]
[0081] Similarly, for the case where Eve announces the measurement result as |R>, the key rate formula is
[0082]
[0083] So, the total key rate formula can be expressed as K = K L +K R . Correspondingly, the total gain and bit error rate can be expressed as Q μ =Q μ,L +Q μ,R , To obtain the lower bound of the secure key rate, using Jensen's inequality, we have
[0084]
[0085] And
[0086]
[0087] Define
[0088]
[0089] Then the final secure key rate formula can be expressed as
[0090]
[0091] Therefore, to obtain the lower bound of the key rate, we need to find the upper bound of , which can be obtained by solving the following constrained optimization problem:
[0092]
[0093] s.t.
[0094]
[0095] and ξ a ≠ ξ b
[0096]
[0097] The security analysis of Protocol II is similar to that of Protocol I. When both Alice and Bob choose the test mode, the joint quantum state ρ of Alice and Bob AB can be expressed as
[0098]
[0099] where represents the probability of obtaining an approximate m - photon number state and, to simplify the formula, we respectively define and
[0100] Eve's collective attack can be described as
[0101]
[0102] where U represents any unitary operation of Eve; |e> E represents Eve's auxiliary system; represents any quantum state corresponding to Eve's announcement of different measurement results |L〉, |R〉 or |N〉. represents the counting rate under different measurement results, satisfying
[0103] By comparing Protocol I and Protocol II, we can obtain
[0104]
[0105] So we can get the following formula
[0106]
[0107] Here we define And to further simplify the formula, we define:
[0108]
[0109]
[0110] Similar to the analysis method of Protocol I, the upper bound of Eve's Holevo information can be obtained as
[0111] Then the final formula for the secure key rate can be expressed as
[0112]
[0113] Therefore, in order to obtain the lower bound of the key rate, it is necessary to find the upper bound of, which can be obtained by solving the following optimization problem with constraints:
[0114]
[0115] s.t.
[0116]
[0117] and ξ b1 ≠ ξ b2
[0118]
[0119] Such as Figures 2 to 5 is the schematic diagram of the result after simulation, Figure 2 is the schematic diagram of the performance simulation of Protocol 1 in the present invention, where the black straight line represents the rate-loss bound, and the curves represent the secure key rates of Protocol 1 when M = 4, 6, 8, 10 respectively. Figure 3 is the performance simulation comparison diagram of Protocol 1 in the present invention and Reference [1] Physical Review Applied 14, 064070 (2020). The solid line and the dotted line represent the simulation results of Protocol 1, and the dashed line represents the simulation result of Reference [1]. Figure 4 is the schematic diagram of the performance simulation of Protocol 2 in the present invention, where the black straight line represents the rate-loss bound, and the curves represent the secure key rates of Protocol 2 when M = 4, 6, 8, 10 respectively. Figure 5 is the performance simulation comparison diagram of Protocol 2 in the present invention and Reference [2] Quantum Information Processing 20, 199 (2021). The solid line and the dotted line represent the simulation results of Protocol 1, and the dashed line represents the simulation result of Reference [2].
[0120] The simulation results show that under the condition of only a small number of discrete phases, the method of the present invention can break the rate-loss bound. At the same time, compared with the two-field quantum key distribution method that requires phase post-selection in the coding mode, the method of the present invention will obtain a higher key rate in the range of low channel loss.
[0121] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and deformations can be made, and these improvements and deformations should also be regarded as the protection scope of the present invention.
Claims
1. A dual-field quantum key distribution method based on a discrete-phase randomized light source, characterized in that It includes three parties, namely the two communication parties Alice and Bob and the untrusted third party Eve. In each round of communication, Alice and Bob choose the encoding mode or the testing mode. If they choose the encoding mode, Alice and Bob will encode classical bits respectively on the phase of the coherent state; if they choose the testing mode, Alice and Bob use a random number to modulate the phase of the coherent state, where M represents the number of phases modulated by Alice and Bob. When there is a subsequent phase selection in the testing mode, the method includes: Step 1: Alice and Bob select an encoding mode or a testing mode in each round of communication. In the encoding mode, a key bit is randomly generated, and a first coherent state is prepared. In the testing mode, a strength and a random number x(y) are randomly selected to prepare a second coherent state; , and a first coherent state is prepared. In the testing mode, a strength and a random number x(y) are randomly selected to prepare a second coherent state; Step 2: Alice and Bob send the prepared first coherent state and second coherent state to the untrusted third party Eve. Eve uses two preset detectors L or R for measurement, announces the measurement results, and obtains successful measurement events according to the measurement results; Step 3: Repeat the above steps. For successful measurement events, Alice and Bob announce their respective selected modes. If both are encoding modes, is used as the raw key. If both are test modes, Alice and Bob respectively announce and . Both parties only save and or of the bit information and calculate the gain; Step 4: Alice and Bob perform error correction and privacy amplification according to the calculated gain to obtain the final secure key; The first coherent state is ( ), representing the optical intensity; The second coherent state is ([[]]END] ), where represents the random numbers selected by Alice and Bob, represents the light intensities selected by Alice and Bob, represents the number of modulation phases of Alice and Bob; The formula for the final secure key is: ， wherein, is the binary Shannon entropy, represents the efficiency of the error correction protocol, and represents the total gain and total bit error rate when the quantum state strength in the coding mode is , represents the Holevo information of Eve.
2. The dual-field quantum key distribution method based on a discrete-phase randomized light source according to claim 1, wherein The measurement results include: only detector L responds, only detector R responds, or no detector responds. If both detectors respond, it is regarded as no detector responding.
3. The dual-field quantum key distribution method based on a discrete-phase randomized light source according to claim 2, wherein The successful measurement events include: only detector L responds or only detector R responds is regarded as a successful measurement event.
4. The dual-field quantum key distribution method based on a discrete-phase randomized light source according to claim 2, wherein In step 3 above, if only detector R responds, Bob needs to invert his key bit .
5. A dual-field quantum key distribution method based on a discrete-phase randomized light source, characterized in that It includes three parties: the communicating parties Alice and Bob, and the untrusted third party Eve. In each round of communication, Alice and Bob choose either the encoding mode or the testing mode. If they choose the encoding mode, Alice and Bob will encode classical bits respectively on the phase of the coherent state; if they choose the testing mode, Alice and Bob use a random number to modulate the phase of the coherent state, where M represents the number of phases modulated by Alice and Bob. When there is no post-selection of phases in the testing mode, the method includes: Step 1: Alice and Bob select an encoding mode or a testing mode in each round of communication. In the encoding mode, a key bit is randomly generated, and a first coherent state is prepared. In the testing mode, a strength and a random number x(y) are randomly selected to prepare a second coherent state; , and a first coherent state is prepared. In the testing mode, a strength and a random number x(y) are randomly selected to prepare a second coherent state; Step 2: Alice and Bob send the prepared first coherent state and second coherent state to the untrusted third party Eve. Eve uses two preset detectors L or R for measurement, announces the measurement results. The measurement results include only detector L responds, only detector R responds, or no detector responds; for the coding mode, if both detectors respond, it is regarded as no detector responding; for the test mode, if both detectors respond, it is regarded as either detector L or detector R randomly responds; among them, only detector L responds or only detector R responds is regarded as a successful measurement event; Step 3: Repeat the above steps. For successful measurement events, Alice and Bob announce their selected corresponding modes. If both are encoding modes, will be used as the raw key. At the same time, if only detector R responds, Bob needs to invert his key bits . If both are test modes, Alice and Bob respectively announce values to calculate the gain; Step 4: Alice and Bob perform error correction and privacy amplification according to the calculated gain to obtain the final secure key; The first coherent state is ( ), representing the optical intensity; The second coherent state is ( ), where represents the random numbers selected by Alice and Bob, represents the optical intensities selected by Alice and Bob, represents the number of modulation phases of Alice and Bob; The formula for the final secure key is: ， Among them, is the binary Shannon entropy, represents the efficiency of the error correction protocol, and represents the total gain and total bit error rate when the quantum state intensity in the coding mode is , represents the Holevo information of Eve.