Multi-ring discrete modulation quantum key distribution method and system based on zero-photon catalysis

Abstract

The present invention relates to the technical field of quantum key distribution, and specifically to a multi-ring discrete modulation quantum key distribution method and system based on zero-photon catalysis. The sender prepares an EPR entangled state. Among them, the A state is subjected to interference and heterodyne detection to obtain two canonical components of the A state. The B state is subjected to zero-photon catalysis and interference to output the B1 state and is sent to the receiver through the transmission channel. The receiver receives the B2 state (i.e., the B1 state after transmission through the channel), and interferes with the B3 state obtained by interfering with the H2 state in the locally generated EPR entangled state. The obtained B3 state is subjected to homodyne or heterodyne detection to obtain the optical signal information. Through post-processing, the receiver generates a secure key consistent with the sender, and repeats this process until the key amount that meets the service requirements is accumulated. The present invention uses zero-photon catalysis operation to replace the traditional photon subtraction scheme, improves the operation success probability while maintaining a similar operation logic, enhances the fidelity of the signal in long-distance transmission, and solves the problem of limited efficiency of the existing photon subtraction technology in practical applications.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum key distribution, and specifically to a multi-ring discrete modulation quantum key distribution method and system based on zero-photon catalysis. Background Technique

[0002] The statements in this part only provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] Quantum key distribution is a key distribution protocol based on the laws of quantum mechanics that ensures its unconditional security. Compared with discrete-variable quantum key distribution protocols, continuous-variable quantum key distribution protocols have received more attention from researchers due to their higher key rate and better compatibility with existing optical links.

[0004] The modulation methods in continuous-variable quantum key distribution protocols mainly include two types: Gaussian modulation and discrete modulation. Since Gaussian modulation can better handle channel noise, using Gaussian modulation can achieve better performance than discrete modulation in short-distance transmission. However, discrete modulation can better resist losses in long-distance transmission, so that in long-distance transmission, the achieved effect and the performance requirements for the infrastructure are better than those of Gaussian modulation.

[0005] The multi-ring discrete modulation method is a technology that can effectively improve the performance of quantum key distribution protocols. It belongs to a type of high-order discrete modulation method, and its performance approaches but does not exceed that of Gaussian modulation.

[0006] In addition, non-Gaussian operations can improve the performance of quantum key distribution protocols under certain conditions. As a type of non-Gaussian operation, the photon subtraction operation has been proven and widely regarded as a method to improve quantum entanglement. However, in actual transmission, the success rate of this method is relatively low. According to relevant statistics, it is difficult to exceed 25%, and the effect is not good in long-distance transmission. Summary of the Invention

[0007] Aiming at the problem that the practical application effect of the photon subtraction operation as a non-Gaussian scheme in quantum key distribution is limited, the present invention provides a multi-ring discrete modulation quantum key distribution method and system based on zero-photon catalysis. The method adopts a zero-photon catalysis operation that has a similar logic to the photon subtraction operation but a higher operation success probability, explores the fusion mechanism between the zero-photon catalysis technology and the multi-ring discrete modulation quantum key distribution protocol, obtains a new covariance matrix by deriving the influence of the zero-photon catalysis operation on the entanglement degree of the EPR entangled state, and calculates and simulates the key rate and the zero-photon catalysis success probability. The results show that compared with the original single-ring and multi-ring discrete modulation continuous variable quantum key distribution protocols, the present invention has improved both in terms of key rate and transmission distance, and the derived fusion mechanism in the present invention has a certain degree of transferability and can be effectively transferred to the research of other quantum secure communications.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] The first aspect of the present invention provides a multi-ring discrete modulation quantum key distribution method based on zero-photon catalysis, including the following steps:

[0010] The sender prepares an EPR entangled state. The A state of the EPR entangled state undergoes interference and heterodyne detection to obtain two canonical components of the A state. The B state of the EPR entangled state undergoes a zero-photon catalysis operation, and through interference with the ground state |0>, the output B1 state is sent to the receiver;

[0011] After the B1 state passes through a channel with a transmission efficiency of T c and an excess noise of ε, it becomes the B2 state and is received by the receiver;

[0012] The receiver receives the B2 state to generate an EPR entangled state. The H2 state of the generated EPR entangled state interferes with the received B2 state optical signal to obtain the B3 state. The B3 state undergoes homodyne detection or heterodyne detection to obtain the information of the corresponding optical signal;

[0013] The receiver generates a secure key consistent with the sender through post-processing based on the information of the optical signal. By repeating the above steps until the number of keys required for the upper-level service is generated.

[0014] Further, the sender uses multi-ring discrete modulation to prepare the EPR entangled state. The constellation diagram of the multi-ring discrete modulation method is regarded as a combination of alphabets, as shown in the following formula:

[0015] ;

[0016] Wherein, represents the position coefficient of the c-th ring relative to the outermost ring, and the indexing direction of the rings is from the inside to the outside, represents the amplitude of the quantum state on the outermost ring, The index representing the relative phase of the k-th quantum state on the c-th ring, The total number of quantum states contained on the c-th ring, The relative offset of the phases of two adjacent quantum states on the c-th ring, The total number of rings in the multi-ring structure.

[0017] Furthermore, the alphabet combination of the multi-ring discrete modulation method and the coherent state Establish the following simplified mapping relationship:

[0018] ; where, , , Represents the index of the x-th state in the c-th ring, m represents the index of all quantum states in the multi-ring structure, Represents the total number of all quantum states in the multi-ring structure.

[0019] Furthermore, the sender performs heterodyne detection on the A state of the EPR entangled state, with a probability To obtain the standard orthogonal basis of the projection measurement , and then obtain two canonical components of the momentum operator and the position operator, which is equivalent to projecting the B state into the coherent state .

[0020] Furthermore, the zero-photon catalytic operation is as follows:

[0021] ;

[0022] Where, , Are the annihilation operator and the creation operator of the B state and the D state respectively, marked Represents the normal ordering of the operator, Is the amplitude gain coefficient.

[0023] Furthermore, the zero-photon catalytic operation on the B state of the EPR entangled state includes: The quantum state in the B state After the zero-photon catalytic operation, under the catalysis of the quantum state , with a probability Catalyze out the quantum states And , specifically: ; where, , Is the zero-photon catalytic operation; The zero-photon catalytic operation makes the amplitude of the incoming coherent state obtain the amplitude gain coefficient with a value of .

[0024] Furthermore, after zero - photon catalysis, the covariance matrix of the AB1 entangled state is obtained, specifically as follows:

[0025] ;

[0026] where, , , , represents the Pauli matrix, represents the identity matrix, represents the square of the amplitude gain coefficient caused by zero - photon catalysis, is the amplitude, is the eigenstate 's eigenvalue, is the intermediate variable that constitutes the eigenstate .

[0027] Furthermore, the quantum state after zero - photon catalysis operation is sent to the receiver through a Gaussian channel. In the Gaussian channel assumption, the B1 state after zero - photon catalysis passes through a channel with transmittance T c , and after transmission through a channel with noise ε, it reaches the receiver and interferes with the EPR entangled state generated by the receiver through a beam splitter to obtain the B3 state; among them, the covariance matrix of the AB3 entangled state is shown as follows:

[0028] ;

[0029] where, , where, a’ , b’ , c’ are intermediate variables, , where, , X line is the channel equivalent noise, represents the Pauli matrix, represents the identity matrix, is the amplitude.

[0030] Furthermore, the receiver generates a secure key that is consistent with the sender's data through a post - processing process, including determining the asymptotic key rate SKR, as shown in the following formula:

[0031] ;

[0032] where, represents the negotiation efficiency between the sender and the receiver, represents the mutual information between the sender and the receiver when the receiver uses homodyne detection, is the detection noise of the receiver, represents the equivalent variance after zero - photon catalysis, represents the mutual information between the eavesdropper and the receiver, T c which is the transmission efficiency.

[0033] The second aspect of the present invention provides a multi-ring discrete modulation quantum key distribution system based on zero-photon catalysis, including a sender and a receiver;

[0034] An EPR generation module, configured to: prepare an EPR entangled state;

[0035] A zero-photon catalysis module, configured to: perform a zero-photon catalysis operation on the B state of the EPR entangled state and interfere with the ground state |0> to output a B1 state;

[0036] A sending module, configured to: send the B1 state output by the zero-photon catalysis module to the receiver;

[0037] The receiver includes:

[0038] A receiving module, configured to: after the B1 state sent by the sender passes through a channel with a transmission efficiency of T c and an excess noise of ε it becomes a B2 state and is acquired by the receiving module;

[0039] A post-processing module, configured to: generate an EPR entangled state according to the received B2 state, the H2 state of the EPR entangled state interferes with the received B2 state optical signal to obtain a B3 state, and perform homodyne detection or heterodyne detection on the B3 state to obtain the information of the corresponding optical signal, and further generate a secure key consistent with the sender.

[0040] Compared with the prior art, the above one or more technical solutions have the following beneficial effects:

[0041] 1. By adopting a zero-photon catalysis operation that has a similar logic to the photon subtraction operation but a higher operation success probability, the entanglement degree of the EPR entangled state is enhanced, the signal fidelity of the entangled state during long-distance transmission can be improved, and the secure key rate and the equivalent tolerable noise are further increased.

[0042] 2. In the quantum key distribution process, multi-ring discrete modulation is used to explore the fusion mechanism of zero-photon catalysis technology and the multi-ring discrete modulation quantum key distribution protocol. By deriving the influence of the zero-photon catalysis operation on the entanglement degree of the EPR entangled state, a new covariance matrix is obtained, and the key rate and the zero-photon catalysis success probability are calculated and simulated. It can improve the information capacity in the signal, and has a higher secure key rate compared with traditional single-ring modulation methods such as 8-state modulation and 4-state modulation. Description of the Drawings

[0043] The accompanying drawings forming a part of this invention are used to provide a further understanding of the invention. The schematic embodiments and descriptions thereof of the invention are used to explain the invention and do not unduly limit the invention.

[0044] Figure 1 It is a schematic diagram of a quantum key distribution mechanism provided by one or more embodiments of the present invention;

[0045] Figure 2 It is a phase diagram of single-loop 4-state modulation provided by one or more embodiments of the present invention;

[0046] Figure 3 It is a phase diagram of single-loop 16-state modulation provided by one or more embodiments of the present invention;

[0047] Figure 4 It is a phase diagram of double-loop 16-state modulation provided by one or more embodiments of the present invention;

[0048] Figure 5 It is a phase diagram of triple-loop 32-state modulation provided by one or more embodiments of the present invention;

[0049] Figure 6 It is a schematic diagram of the performance simulation of multi-switching loop modulation without zero-photon catalysis during quantum key distribution provided by one or more embodiments of the present invention;

[0050] Figure 7 It is a schematic diagram of the performance simulation of multi-switching loop modulation after zero-photon catalysis during quantum key distribution provided by one or more embodiments of the present invention. Detailed implementation manners

[0051] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0052] It should be noted that the following detailed descriptions are all exemplary and are intended to provide a further description of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0053] Term explanation:

[0054] Quantum Key Distribution (QKD) is a technology that uses the principles of quantum mechanics to achieve secure communication. Its core goal is to enable two communicating parties to generate and share an absolutely secure key in the presence of a possible eavesdropper (Eve). This key can then be used to encrypt and decrypt sensitive information (such as through encryption methods like "one-time pad"). Its core principle is the quantum no-cloning theorem and the Heisenberg uncertainty principle.

[0055] Quantum no-cloning theorem: Quantum states cannot be precisely replicated, and any eavesdropping behavior will interfere with the quantum state, thus being detected by both communication parties.

[0056] Heisenberg uncertainty principle: Measuring a quantum system will perturb its state. For example, when measuring the polarization state of a photon, choosing the wrong basis vector (such as measuring a diagonally polarized photon with a rectangular basis) will introduce errors.

[0057] EPR entangled state refers to the maximum entangled state of a two-particle (or multi-particle) system. Initially proposed by Einstein, Podolsky, and Rosen in 1935 (the famous EPR paradox) to question the completeness of quantum mechanics. Later, such states were experimentally verified and became one of the core resources in quantum information science (such as quantum communication and quantum computing).

[0058] Photon subtraction operation, a typical non-Gaussian operation in the process of quantum key distribution, mainly used to enhance the entanglement characteristics of quantum states or optimize the transmission performance of quantum key distribution protocols. The core idea is to change the probability distribution of the original quantum state by removing (subtracting) one or more photons from the optical field, making it transform from a Gaussian state to a non-Gaussian state, thereby improving the availability of quantum resources.

[0059] As introduced in the background technology, the practical application effect of the photon subtraction operation as a non-Gaussian scheme in quantum key distribution is limited. Therefore, the following embodiments present a multi-ring discrete modulation quantum key distribution method based on zero-photon catalysis, which adopts a zero-photon catalysis operation with a logic similar to that of the photon subtraction operation but a higher operation success probability. It explores the fusion mechanism between zero-photon catalysis technology and the multi-ring discrete modulation quantum key distribution protocol. By deriving the influence of the zero-photon catalysis operation on the entanglement degree of the EPR entangled state, a new covariance matrix is obtained, and the key rate and the zero-photon catalysis success probability are calculated and simulated. The results show that compared with the original single-ring and multi-ring discrete modulation continuous variable quantum key distribution protocols, the present invention has improved both in terms of key rate and transmission distance, and the derived fusion mechanism in the present invention has a certain degree of transferability and can be effectively transferred to the research of other quantum secure communications.

[0060] The success probability of the photon subtraction operation and the probability of zero-photon catalysis are both derived from the formulas in existing literature. The mechanisms of these two operations are similar. The success rate of the photon subtraction operation is derived from the statistical values of the input state and output state of the photon subtraction device. The low success rate can be attributed to the inherent defects of the photon subtraction operation mechanism, which is a problem of the mechanism. The zero-photon catalysis operation introduced in this scheme also has its success rate derived from the statistical values of the input state and output state of the zero-photon catalysis device, and it has a higher success rate compared to the photon subtraction operation.

[0061] Example 1:

[0062] In this embodiment, a multi-ring discrete modulation quantum key distribution method based on zero-photon catalysis is implemented between a sender and a receiver connected by an optical fiber link;

[0063] The sender includes:

[0064] An EPR generation module (MR-Modulator) for generating an EPR entangled state;

[0065] A multi-ring modulation module for modulating quantum state signals;

[0066] A photon detection module for detecting the signal of the A state of the EPR entangled state;

[0067] A zero-photon catalysis module for performing zero-photon catalysis operation on the B state of the EPR entangled state to improve the entanglement degree of photon signals.

[0068] The receiver includes:

[0069] An optical beam splitter for interfering the received photon signal with the EPR entangled state generated by the receiver;

[0070] A photon detection module for performing homodyne or heterodyne detection on the interfered signal.

[0071] The EPR entangled state is bimodal, and the two modes are the A state and the B state respectively. According to the principles of quantum mechanics, when the A state is measured, the value of the B state can be obtained simultaneously. This phenomenon can be understood as quantum entanglement, which is the origin of the word "entanglement" in the EPR entangled state. In the security analysis of quantum key distribution, existing literature often uses a protocol based on entanglement (for convenience of security analysis) equivalent to the one based on preparation and measurement (for convenience of practical implementation) to calculate the secure key rate of the protocol. The subsequent B1 state is the quantum state output after the zero-photon catalysis operation on the B state is successful; the B2 state is the quantum state output after transmission through a Gaussian channel; the H2 state and the H3 state are quantum states that play an auxiliary role for the receiver to detect the B2 state. The H2 state is sent to the optical beam splitter BS2 to interfere with the B2 state, thereby generating the H1 state and the B3 state. The B3 state is a quantum state that is easier to measure after interference. These states are all quantum states with specific meanings.

[0072] Combined with Figure 1 Explaining the quantum key distribution mechanism includes the following steps:

[0073] Step 1: The sender prepares an EPR entangled state. Inside the sender, the A state of the EPR entangled state is interfered with the vacuum state vacuum, and then heterodyne detection is performed by the heterodyne detection module Het1 to obtain two canonical components of the A state (the momentum component X A and the position component P A ). Subsequently, the other state of the EPR entangled state passes through a multi-loop modulator and is modulated according to the encoded information to obtain the B state;

[0074] Step 2: The sender sends the prepared B state of the two-mode squeezed vacuum state to the zero-photon catalytic module to interfere with the same ground state |0> and perform the zero-photon catalytic operation. If the switching photodetector responds to the |0> state, it indicates that the zero-photon catalytic operation is successful, and then the B1 state is output and proceeds to Step 3. If not, it indicates that the zero-photon catalytic operation fails, and Steps 1 and 2 need to be repeated;

[0075] Step 3: After the B1 state passes through a channel with a transmission efficiency of T c and an excess noise of ε, it becomes the B2 state. In the transmission channel, assuming that the eavesdropper will perform a joint eavesdropping attack, the eavesdropper will independently interact the B1 state with its own specific system and store the result after the interaction in the quantum memory. The eavesdropper will not only eavesdrop on the quantum signal but also eavesdrop on the classical communication signal. During the post-processing process, the sender and the receiver will send classical information for various post-processing operations, and the eavesdropping party will also extract the security key based on the content of the eavesdropped post-processing process and the data in the quantum memory to obtain the key. Channel noise and channel transmission efficiency are the preconditions for the eavesdropper to obtain the eavesdropping opportunity;

[0076] Step 4: The receiver receives the B2 state to generate an EPR entangled state, interferes the H2 state with the received optical signal to obtain the B3 state, and by using the homodyne detection module Hom2 to perform homodyne detection on the B3 state, the position component X B or the momentum component P B of the canonical component can be obtained, or by using the heterodyne detection module Het2 to perform heterodyne detection, both the position component X B and the momentum component P B can be obtained simultaneously;

[0077] Step 5: The receiver generates a security key that is consistent with the sender's data through the post-processing process;

[0078] Step 6: Repeat Steps 1 to 4 until the number of keys that meet the requirements of the upper-level service is generated.

[0079] The above process gives the key generation processes of the sender and the receiver. Among them, steps 1 to 4 are the communication processes on the quantum link, while the post-processing process (the general term for a series of operations) in step 5 is the communication process on the classical communication link. The sender and the receiver transmit quantum state information through the quantum link and obtain a secure key through the post-processing process based on the classical communication link.

[0080] Regarding the detection of eavesdropping by the two communication parties: The sender and the receiver estimate and calculate the final available key rate based on the transmission efficiency and noise of the channel. The eavesdropping behavior can be transformed into an equivalent increase in channel noise, which will inevitably cause a decrease in the actual secure key rate. When the key rate calculated by the two communication parties is abnormally higher than the key rate statistically obtained in the actual key generation process, it is considered that eavesdropping has occurred. Therefore, quantum key distribution has the ability to detect eavesdropping and takes certain corresponding measures against the snooping behavior. The corresponding measures are not within the scope of this solution and will not be elaborated in this solution.

[0081] As a further implementation method, the modeling process of the multi-ring discrete modulation of the sender and the generation processes of the A state and B state of the EPR entangled state are as follows:

[0082] From the perspective of preparation and measurement, the constellation diagram of the multi-ring discrete modulation method is regarded as consisting of the following alphabet:

[0083] ;

[0084] Among them, represents the position coefficient of the c-th ring relative to the outermost ring. The indexing direction of the rings is from the inside to the outside. represents the amplitude of the quantum state on the outermost ring. represents the index of the relative phase of the k-th quantum state on the c-th ring. represents the total number of quantum states contained on the c-th ring. represents the relative offset of the phases of two adjacent quantum states on the c-th ring. represents the total number of rings in the multi-ring structure. e is a constant. i is the imaginary part of the complex number.

[0085] The constellation diagram of the multi-ring discrete modulation method is as Figures 2 - 5As shown, each figure is a "phase diagram of coherent states". Coherent states are quantum states in which neither the momentum component nor the position component is squeezed. The amplitude-phase binary pair of a quantum state can be converted into the corresponding momentum component-position component binary pair, and the canonical components of coherent states can be encoded so that coherent states carry information. Each point in the figure is a coherent state, and points with the same color belong to the same ring. The abscissa X in the figure represents the momentum component attribute in the canonical components, and the ordinate P represents the position component attribute in the canonical components. Specifically, Figure 2 is the phase diagram of single-ring 4-state modulation, Figure 3 is the phase diagram of single-ring 16-state modulation, Figure 4 is the phase diagram of double-ring 16-state modulation, Figure 5 is the phase diagram of triple-ring 32-state modulation.

[0086] Taking Figure 5 as an example to explain the "phase diagram of coherent states", Figure 5 has three rings. From the inside out, it is composed of 4 green coherent states, 12 red coherent states, and 16 blue coherent states. The amplitude of the outermost ring is uniformly set to , so the amplitude of the innermost ring is set to , and the amplitude of the second ring is set to . is the phase interval between adjacent quantum states on the second ring. According to the expressions related to coherent states, different phases and amplitudes are selected, and the coherent states are arranged on the Figure 3 shown phase diagram.

[0087] As a further implementation, the following simplified mapping relationship is established between the above alphabet and coherent states:

[0088] ;

[0089] where , , where represents the index of the x-th state in the c-th ring, m represents the index of all quantum states in the multi-ring structure, represents the total number of all quantum states in the multi-ring structure.

[0090] The information obtained by the sender is a mixed state in the following form:

[0091] ;

[0092] where represents the probability of preparing the m-th quantum state.

[0093] As a further implementation, the modulation variance is set.

[0094] As a further implementation, the above modeling can be converted into an entanglement-based version, as shown in the following equation:

[0095] ;

[0096] where, , represents the orthonormal basis used in projective measurement.

[0097] As a further implementation, the sender performs heterodyne detection on the A state, with probability to obtain and then obtains two canonical components of the momentum operator and the position operator. This process is equivalent to projecting the B state into a coherent state . A coherent state is a quantum state in which neither the momentum component nor the position component is squeezed. Its canonical components can be encoded to carry information. Through quantum detection, different canonical components can be read, and then the carried information can be analyzed. It should be noted that according to the quantum uncertainty principle of quantum mechanics, the position component and the momentum component cannot be measured precisely simultaneously.

[0098] As a further implementation, in the purification process of the mixed state , by performing spectral decomposition on it, the following equation is obtained:

[0099] ;

[0100] where, ; is the eigenstate of the mixed state system, is the eigenvalue of the eigenstate , is the intermediate variable that constitutes the eigenstate , n is the number of photons in the quantum optical field, used to represent the photon number state.

[0101] where, represents the average amplitude, is used for normalization.

[0102] As a further implementation, the covariance matrix of the AB entangled state is obtained, as shown in the following equation:

[0103] ;

[0104] where, , , represents the Pauli matrix, represents the identity matrix, ;

[0105] where, When m = N - 1, m = 0.

[0106] As a further implementation, through zero - photon catalytic operation, the entanglement of the AB entangled state is enhanced. The zero - photon catalytic operation can be regarded as the following equivalent operator:

[0107] ;

[0108] where , |0>D<0| is the projection of the D state onto the ground state |0>, are the annihilation operator and creation operator of the B state and D state respectively, and the annotation represents the normal ordering of the operator. Tr [ ] is the trace operation, and exp[ ] is the exponential function with the natural number e as the base.

[0109] The quantum state in the B state After being input into the photon - catalytic module, under the catalysis of the quantum state , it will successfully catalyze the quantum state and and with a probability , where .

[0110] Therefore, from the perspective of preparation and measurement, the process of the B state undergoing zero - photon catalytic operation can be equivalent to:

[0111] .

[0112] In this embodiment, the zero - photon catalytic operation gives the amplitude of the incoming coherent state a gain coefficient with a value of . The covariance matrix of the AB1 entangled state after zero - photon catalysis is represented by the following equation:

[0113] ;

[0114] where , , , The derivation steps of other intermediate variables in (note the amplitude gain coefficient caused by zero - photon catalysis) are the same as those described above. For example, , so it will not be elaborated here.

[0115] Successful zero-photon catalysis can increase the amplitude of the coherent state. It should be noted that this is an equivalent effect after modeling. Physically, the zero-photon catalysis operation can improve the coherence and entanglement of the EPR entangled state. The coherence and entanglement of the EPR entangled state will decrease with the increase of the transmission distance. Therefore, the zero-photon catalysis operation can improve the coherence and entanglement during long-distance transmission, thereby increasing the secure key rate, that is, the physical effect of zero-photon catalysis.

[0116] As a further implementation, the quantum state after the zero-photon catalysis operation is sent to the receiver through a Gaussian channel. In the Gaussian channel assumption, the B1 state after zero-photon catalysis passes through a channel with a transmittance of T c , and after passing through a channel with noise ε, it reaches the receiver and interferes with the EPR entangled pair generated by the receiver by the beam splitter BS2 to obtain the B3 state. Thus, the covariance matrix of the AB3 entangled state is obtained as shown in the following formula:

[0117] ;

[0118] Among them, , a’ , b’ , c’ are intermediate variables, , among which, , X line is the channel equivalent noise.

[0119] This scheme realizes the integration with the zero-photon catalysis operation compared with the prior art. The content of this covariance matrix is a further inference based on the influence of the modeled zero-photon catalysis operation on the amplitude of the quantum state. The relevant experimental results show that the zero-photon catalysis operation can further improve the performance of multi-ring discrete modulation.

[0120] As a further implementation, the calculation formula for the asymptotic key rate SKR is given by the following equation:

[0121] ;

[0122] Among them, represents the negotiation efficiency between the sender and the receiver, , represents the mutual information between the sender and the receiver when the receiver uses homodyne detection, is the detection noise of the receiver, represents the equivalent variance after zero-photon catalysis, represents the mutual information between the eavesdropper and the receiver; is the covariance matrix 's symplectic eigenvalue, is the symplectic eigenvalue of the covariance matrix of the B3 state when performing detection.

[0123] Among them, ;

[0124] ;

[0125] ;

[0126] For the case of homodyne detection, , ;

[0127] Among them, , .

[0128] The quantum key distribution process given by this scheme uses multi-ring discrete modulation, which can increase the information capacity in the signal. Therefore, compared with traditional single-ring modulation methods such as 8-state modulation and 4-state modulation, the secure key rate is higher.

[0129] This scheme performs zero-photon catalysis operation on quantum states, enhances the entanglement degree of the EPR entangled state, can improve the signal fidelity of the entangled state during long-distance transmission, and further increases the secure key rate and the equivalent tolerable noise.

[0130] In this scheme, successful zero-photon catalysis can increase the amplitude of the coherent state. It should be noted that this is the equivalent effect after modeling. Physically, the zero-photon catalysis operation can improve the coherence and entanglement of the EPR entangled state. The coherence and entanglement degrees of the EPR entangled state will decrease with the increase of the transmission distance. Therefore, the zero-photon catalysis operation can improve the coherence and entanglement degrees during long-distance transmission, and thus increase the secure key rate. This is the physical effect of zero-photon catalysis. This scheme proves that for different multi-ring discrete modulation protocols, there is a certain performance improvement.

[0131] Experiment. Under the condition that the conventional experimental parameters are channel noise 0.01 SNU (SNU, shot noise unit), channel fading 0.2 / km, receiver detector noise 0.05, receiver detector efficiency 0.6, sender and receiver reconciliation efficiency 0.9, and the secure key rate is 10-6 (bit / pulse), for all modulation methods, the optimal modulation variance at 20 km is taken, and the maximum transmission distance (km) is as Figure 6 shown in Table 1.

[0132] Table 1 Simulation experimental data before using zero-photon catalysis

[0133]

[0134] If the zero-photon catalysis technology is used, the efficiency of the zero-photon catalysis operation Take the optimal value, then the maximum transmission distance (km) obtained in the simulation performance is as Figure 7 shown in Table 2.

[0135] Table 2 Simulation experiment data after using zero-photon catalysis

[0136]

[0137] According to Figure 6 and Figure 7 , as well as Table 1 and Table 2, it can be seen that after applying the zero-photon catalysis operation, for 2-ring 16-state modulation and 3-ring 32-state modulation with the same ring spacing, the performance can be improved by 19.92% and 33.69% respectively. At the optimal ring spacing (parameters are k1 = 0, and k1 = 0, k2 = 0.35 respectively), the performance can be improved by 8.94% and 34.01% respectively. Through analysis, it can be known that the zero-photon catalysis operation can effectively improve the performance of multi-ring discrete modulation methods. From the analysis of the security key rate curve, the zero-photon catalysis operation can effectively improve the security key rate during long-distance transmission.

[0138] In this experiment, simulation experiments were carried out using software (such as matlab2022b). For the simulation of multi-ring modulation, there is no analytical solution that can be simplified for implementation. Therefore, this scheme carried out a 1:1 modeling replication of the mathematical expressions of quantum states. In the exploration of the fusion mechanism, in the expression of the success probability of the zero-photon catalysis operation, this scheme proposed a method of using the average modulation variance to replace the weighted value of the modulation variance of the quantum states of the multi-ring structure, realizing the fusion of the success probability calculation of the multi-ring modulation method and the zero-photon catalysis operation. In the exploration of fusion, the derivation of the covariance matrix is the key point, and how to strip the model irrelevant to the entanglement degree in the modeling is the difficult point. Through continuous reasoning and testing, the scheme successfully extracted the steps related to the entanglement degree and integrated the model of zero-photon catalysis into it, and finally overcome the difficulty of constructing a new covariance matrix.

[0139] Example 2:

[0140] A multi-ring discrete modulation quantum key distribution system based on zero-photon catalysis, including a sender and a receiver;

[0141] An EPR generation module, configured to: prepare an EPR entangled state;

[0142] A zero-photon catalysis module, configured to: perform a zero-photon catalysis operation on the B state of the EPR entangled state and interfere with the ground state |0> to output the B1 state;

[0143] A sending module, configured to: send the B1 state output by the zero-photon catalysis module to the receiver;

[0144] The receiver includes:

[0145] A receiving module, configured to: After the B1 state sent by the sender passes through a channel with a transmission efficiency of T c and an excess noise of ε , it becomes the B2 state and is acquired by the receiving module;

[0146] A post-processing module, configured to: Generate an EPR entangled state according to the received B2 state, the H2 state of the EPR entangled state interferes with the received B2 state optical signal to obtain the B3 state, and the B3 state is subjected to homodyne detection or heterodyne detection to obtain the information of the corresponding optical signal, and further generate a security key consistent with the sender.

[0147] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A multi-ring discrete modulation quantum key distribution method based on zero-photon catalysis, characterized in that It includes the following steps: The sender prepares an EPR entangled state. The A state of the EPR entangled state undergoes interference and heterodyne detection to obtain two canonical components of the A state. The B state of the EPR entangled state undergoes a zero-photon catalysis operation. By interfering with the ground state |0>, the output B1 state is sent to the receiver; The B1 state is transmitted through a channel with transmission efficiency T c and over a channel with excess noise ε, and then becomes the B2 state and is received by the receiving party; The receiver receives the B2 state to generate an EPR entangled state. The B3 state obtained by interfering the H2 state of the generated EPR entangled state with the received B2 state optical signal undergoes homodyne detection or heterodyne detection to obtain the information of the corresponding optical signal; The receiver generates a secure key consistent with the sender through post-processing based on the information of the optical signal. By repeating the above steps until the number of keys required for the upper-level service is generated; Among them, the sender uses multi-ring discrete modulation to prepare the EPR entangled state. The constellation diagram of the multi-ring discrete modulation method is regarded as a combination of alphabets, as shown in the following formula: ； Among them, represents the position coefficient of the c-th ring relative to the outermost ring, and the indexing direction of the rings is from the inner side to the outer side, represents the amplitude of the quantum state on the outermost ring, represents the index of the relative phase of the k-th quantum state on the c-th ring, represents the total number of quantum states contained on the c-th ring, represents the relative offset of the phases of two adjacent quantum states on the c-th ring, represents the total number of rings in the multi-ring structure, and i is the imaginary part of the complex number; Among them, the zero-photon catalytic operation on the B state of the EPR entangled state includes: the quantum state in the B state After the zero-photon catalytic operation, under the catalysis of the quantum state with a probability of catalyzes the quantum states and , specifically: ; among them, , is the zero-photon catalytic operation; the zero-photon catalytic operation makes the amplitude of the incoming coherent state obtain an amplitude gain coefficient with a value of .

2. The multi-ring discrete modulation quantum key distribution method based on zero-photon catalysis according to claim 1, wherein Alphabet Combinations and Coherent States of Multi-Ring Discrete Modulation Modes The following simplified mapping relationship is established: ; among them, , , represents the index of the x-th state in the c-th ring, and m represents the index of all quantum states in the multi-ring structure. represents the total number of all quantum states of the multi-ring structure.

3. The multi-ring discrete modulation quantum key distribution method based on zero-photon catalysis according to claim 1, characterized in that, The sender performs heterodyne detection on the A state of the EPR entangled state, with a probability of obtaining the standard orthogonal basis for projective measurement , and then obtaining two canonical components of the momentum operator and the position operator, which is equivalent to projecting the B state into a coherent state .

4. The multi-ring discrete modulation quantum key distribution method based on zero-photon catalysis according to claim 1, wherein The zero-photon catalysis operation is as shown in the following formula: ； Among them, , are the annihilation operator and creation operator in the B state and D state respectively, marked indicating the normal ordering of the operator, is the amplitude gain coefficient, Tr [ ] is the trace operation, and exp[ ] is the exponential function with the natural number e as the base.

5. The multi-ring discrete modulation quantum key distribution method based on zero-photon catalysis according to claim 1, characterized in that After zero-photon catalysis, the covariance matrix of the AB1 entangled state is obtained, specifically: ； Among them, , , , represent Pauli matrices, represents the identity matrix, represents the square of the amplitude gain coefficient caused by zero-photon catalysis, is the amplitude of the quantum state on the outermost ring, i.e., the amplitude, is the eigenstate 's eigenvalue, is the intermediate variable that constitutes the eigenstate .

6. The multi-ring discrete modulation quantum key distribution method based on zero-photon catalysis according to claim 1, characterized in that, The quantum state after zero-photon catalytic operation is sent to the receiver through a Gaussian channel. In the Gaussian channel assumption, the B1 state after zero-photon catalysis passes through a channel with a transmittance of T c , and after transmission through a channel with a noise of ε, it reaches the receiver and interferes with the EPR entangled state generated by the receiver by a beam splitter to obtain the B3 state; among them, the covariance matrix of the AB3 entangled state is shown in the following formula: ； Among them, wherein, a’ , b’ , c’ are intermediate variables, , , X line is the channel equivalent noise, is a mixed state, is the probability of the m-th quantum state, T c is the transmission efficiency, ε is the noise, represents the Pauli matrix, represents the identity matrix, is the average amplitude.

7. The multi-ring discrete modulation quantum key distribution method based on zero-photon catalysis according to claim 1, characterized in that, The receiver generates a secure key consistent with the sender in terms of data through the post-processing process, including determining the asymptotic key rate SKR, as shown in the following formula: ； Among them, represents the negotiation efficiency between the sender and the receiver, represents the mutual information between the sender and the receiver when the receiver uses homodyne detection, is the detection noise of the receiver, represents the equivalent variance after zero-photon catalysis, represents the mutual information between the eavesdropper and the receiver, T c is the transmission efficiency.

8. A multi-ring discrete modulation quantum key distribution system based on zero-photon catalysis for implementing the method according to any one of claims 1-7, characterized in that It includes a sender and a receiver; The sender includes: An EPR generation module configured to: prepare an EPR entangled state; A zero-photon catalysis module configured to: perform a zero-photon catalysis operation on the B state of the EPR entangled state, interfere with the ground state |0>, and output the B1 state; A sending module configured to: send the B1 state output by the zero-photon catalysis module to the receiver; The receiver includes: A receiving module, configured to: After the B1 state sent by the sender passes through a channel with a transmission efficiency of T c and an excessive noise of ε , it becomes the B2 state and is acquired by the receiving module; A post-processing module configured to: generate an EPR entangled state according to the received B2 state. The B3 state obtained by interfering the H2 state of the EPR entangled state with the received B2 state optical signal undergoes homodyne detection or heterodyne detection to obtain the information of the corresponding optical signal, and further generate a secure key consistent with the sender.

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