An efficient quantum key generation method based on entangled states and stabilizer codes

Abstract

The application relates to an efficient quantum key generation method based on entangled states and stabilizer codes, which comprises the following steps: constructing multiple groups of original GHZ entangled states, distributing a first particle sequence and a second particle sequence to a sender, and distributing a third particle sequence to a receiver; applying a first unitary operation and a second unitary operation to each particle in the first particle sequence and the second particle sequence respectively, and combining the third particle sequence to form distinguishable GHZ entangled states; preparing multiple check particles to obtain a check sequence and a corresponding preparation basis, and pairing to form multiple composite particle groups; encoding each composite particle group through a quantum error correction code to obtain a composite quantum system; decoding the composite quantum system through the quantum error correction code, retaining an effective particle group to perform GHZ basis measurement, and generating a final key. The application can improve the key generation efficiency, has a single-bit error correction capability, is strong against noise, and has simple and efficient eavesdropping detection.

Description

Technical Field

[0001] This application relates to the field of digital information transmission technology, and in particular to an efficient quantum key generation method based on entangled states and stable subcodes. Background Technology

[0002] Quantum key distribution is an important research direction in the field of quantum communication. Since Bennett and Brassard proposed the BB84 protocol in 1984, information security mechanisms based on the fundamental principles of quantum mechanics have received widespread attention. Among them, quantum key distribution protocols based on entangled states utilize the non-local correlation properties of EPR pairs, enabling both communicating parties to confirm the security of the channel through Bell's inequality test, theoretically achieving unconditionally secure key sharing. With the continuous development of quantum information technology, the application of multi-particle entangled states, such as GHZ (Greenberger-Horne-Zeilinger) entangled states, in quantum communication has gradually become a research hotspot.

[0003] In existing technologies, EPR (Einstein-Podolsky-Rosen) entangled pairs are typically used as information carriers. Each communicating party holds one particle from the EPR pair. By randomly selecting measurement bases and retaining measurement results with identical bases, each EPR pair can generate a single-bit original key, enabling key distribution based on quantum entanglement. However, this method generates only one key per entangled pair, resulting in low key generation efficiency. Furthermore, entangled states are susceptible to channel and device noise during transmission, leading to decoherence and discrepancies between the key obtained by the receiver and the information encoded by the sender. Additionally, Bell inequality-based eavesdropping detection requires calculating correlation functions under multiple different measurement bases, making the implementation cumbersome and demanding high precision from experimental equipment.

[0004] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0005] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this disclosure is to provide an efficient quantum key generation method based on entangled states and stable subcodes, thereby overcoming, to at least some extent, one or more problems caused by the limitations and defects of related technologies.

[0007] This application provides an efficient quantum key generation method based on entangled states and stable subcodes, including: The sender constructs multiple sets of original GHZ entangled states, assigns the three particles in each set of original GHZ entangled states to the first particle sequence, the second particle sequence, and the third particle sequence, respectively, and distributes the first particle sequence and the second particle sequence to the sender, and the third particle sequence to the receiver; The sender applies a first unitary operation and a second unitary operation to each particle in the first particle sequence and the second particle sequence it holds, respectively, to obtain the operated first particle sequence and the operated second particle sequence, and forms a distinguishable GHZ entangled state with the third particle sequence. The sender randomly selects Z-based or X-based to prepare multiple check particles, obtains a check sequence and the corresponding preparation base, and pairs each check particle in the check sequence with the particles in the operated first particle sequence and the particles in the operated second particle sequence to form multiple composite particle groups; The sender encodes each of the composite particle groups using quantum error correction codes to obtain the encoded composite quantum system, and then transmits the composite quantum system to the receiver. The receiver decodes the composite quantum system using the quantum error correction code, randomly selects the comparison results between the measurement basis and the preparation basis, retains the particle group corresponding to the same position of the measurement basis and the preparation basis as the effective particle group, and performs GHZ basis measurement on the particles in the effective particle group corresponding to the same distinguishable GHZ entangled state to generate the final key.

[0008] The technical solution provided in this application may include the following beneficial effects: This application presents an efficient quantum key generation method based on entangled states and stable subcodes. It focuses solely on the generation of quantum keys, without imposing constraints on the statistical characteristics, arrangement, or subsequent algorithms of the keys. The method enables the sender to apply first and second unitary operations to its first and second particle sequences, respectively, forming distinguishable GHZ entangled states with a third particle sequence. Each GHZ entangled state encodes a three-bit key, increasing key generation efficiency to three times that of traditional EPR pairing schemes. Furthermore, it encodes each composite particle group using quantum error-correcting codes, leveraging the error-correcting capability of the [[8,3,3]] Gottesman quantum error-correcting code to detect and correct single-bit errors during transmission, enhancing the system's tolerance to channel and device noise and improving the fidelity of the final key. Simultaneously, by preparing a verification sequence and pairing it with the manipulated particle sequences, the receiver compares the consistency between the measurement basis and the prepared basis after decoding. Valid particle groups at the same positions in the basis are retained for GHZ basis measurement, achieving error rate-based eavesdropping detection, avoiding complex Bell inequality verification, and simplifying the security detection process.

[0009] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0010] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0011] Figure 1 A flowchart illustrating an efficient quantum key generation method based on entangled states and stable subcodes in an exemplary embodiment of this disclosure is shown. Figure 2 This illustration shows a schematic diagram of the distribution of multiple GHZ entangled states in an efficient quantum key generation method based on entangled states and stable subcodes according to an exemplary embodiment of this disclosure; Figure 3 A detailed flowchart of step S100 of the efficient quantum key generation method based on entangled states and stable subcodes in an exemplary embodiment of this disclosure is shown. Figure 4 This diagram illustrates the efficient quantum key generation method based on entangled states and stable subcodes in an exemplary embodiment of this disclosure, performing unitary operations on the first and second particle sequences. Figure 5 A detailed flowchart of step S200 of the efficient quantum key generation method based on entangled states and stable subcodes in an exemplary embodiment of this disclosure is shown. Figure 6 A detailed flowchart of step S300 of the efficient quantum key generation method based on entangled states and stable subcodes in an exemplary embodiment of this disclosure is shown. Figure 7 A schematic diagram of the Gottesman quantum error-correcting code circuit for an efficient quantum key generation method based on entangled states and stable subcodes in an exemplary embodiment of this disclosure is shown. Figure 8 A detailed flowchart of step S400 of the efficient quantum key generation method based on entangled states and stable subcodes in an exemplary embodiment of this disclosure is shown. Figure 9 This diagram illustrates the overall key generation process of an efficient quantum key generation method based on entangled states and stable subcodes in an exemplary embodiment of this disclosure. Figure 10 A detailed flowchart of step S500 of the efficient quantum key generation method based on entangled states and stable subcodes in an exemplary embodiment of this disclosure is shown. Detailed Implementation

[0012] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0013] Furthermore, the accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0014] This example implementation first provides an efficient quantum key generation method based on entangled states and stable subcodes. This method can be applied to terminal devices, such as quantum communication transceivers, quantum network user terminals, and data center server terminals. (Reference) Figure 1 As shown, the method may include the following steps: Step S100: The sender constructs multiple sets of original GHZ entangled states, assigns the three particles in each set of original GHZ entangled states to the first particle sequence, the second particle sequence, and the third particle sequence, respectively, and distributes the first particle sequence and the second particle sequence to the sender, and the third particle sequence to the receiver.

[0015] Step S200: The sender applies a first unitary operation and a second unitary operation to each particle in the first particle sequence and the second particle sequence it holds, respectively, to obtain the operated first particle sequence and the operated second particle sequence, and forms a distinguishable GHZ entangled state with the third particle sequence.

[0016] Step S300: The sender randomly selects Z-based or X-based to prepare multiple check particles, obtains a check sequence and the corresponding preparation base, and pairs each check particle in the check sequence with the particles in the operated first particle sequence and the particles in the operated second particle sequence to form multiple composite particle groups.

[0017] Step S400: The sender encodes each of the composite particle groups using quantum error correction codes to obtain the encoded composite quantum system, and then transmits the composite quantum system to the receiver.

[0018] Step S500: The receiver decodes the composite quantum system using the quantum error correction code, randomly selects the comparison results between the measurement basis and the preparation basis, retains the particle group corresponding to the same position of the measurement basis and the preparation basis as the effective particle group, and performs GHZ basis measurement on the particles in the effective particle group corresponding to the same distinguishable GHZ entangled state to generate the final key.

[0019] The aforementioned method can encode each GHz entangled state into a three-bit key during quantum key distribution, increasing key generation efficiency to three times that of traditional EPR pair schemes. By introducing the [[8,3,3]] Gottesman quantum error-correcting code, single-bit errors during transmission are detected and corrected, enhancing the system's tolerance to channel and device noise. A verification sequence-based eavesdropping detection mechanism is employed, which can determine the presence of eavesdropping by comparing the consistency between the preparation basis and the measurement basis, avoiding complex Bell inequality verification operations and simplifying the security detection process. This application simultaneously achieves high-efficiency, high-reliability, and high-security quantum key distribution.

[0020] Below, we will refer to Figures 2 to 10 The steps of the method described above in this example embodiment will be explained in more detail.

[0021] In step S100, the sender constructs multiple sets of original GHZ entangled states, assigns the three particles in each set of original GHZ entangled states to the first particle sequence, the second particle sequence, and the third particle sequence, respectively, and distributes the first particle sequence and the second particle sequence to the sender, and the third particle sequence to the receiver.

[0022] It should be noted that the maximum entanglement of the three particles in the original GHZ entangled state ensures the feasibility of state differentiation after unitary operations. The three particles of each GHZ state are assigned to three independent sequences, with the first and second sequences controlled by the sender and the third sequence by the receiver. This ensures that subsequent unitary operations only apply to the particles held by the sender, while maintaining entanglement across sequences. This distribution method supports batch processing, transmitting N sets of GHZ states at once, avoiding the repetitive overhead of multiple entanglement distributions.

[0023] Specifically, to generate a multi-bit key, this method requires distributing multiple sets of GHZ entangled states to both the sender Alice and the receiver Bob. These entangled states are divided into three sequences, denoted as sequence K1, K2, and K3. During distribution, sequences K1 and K2 are sent to Alice, and the remaining sequence K3 is sent to Bob. The distributed GHZ states remain entangled, and the number N of GHZ states in the sequence is determined based on the length of the key to be generated. Generally, the number N is greater than the length of the key to be generated. A distribution diagram is shown below. Figure 2 As shown. This distribution method is more convenient than the method of distributing a GHz entangled state each time, generating a small portion of the key, and then distributing another GHz entangled state and generating another small portion of the key after the distribution is complete.

[0024] In one embodiment, such as Figure 3 As shown, step S100 may include the following sub-steps: In step S110, the number of required GHZ entangled states is determined based on the final key length to be generated; wherein the number of the original GHZ entangled states is greater than the final key length.

[0025] It should be noted that the number of GHZ entangled states determines the length of the final key. Each GHZ state is subsequently processed to generate a three-bit key, requiring more than one-third of the final key length. Once the number of GHZ entangled states is determined, the total number of particles, the number of unitary operations, the number of check particles, and the number of encoding operations for the entire protocol are also determined, and these are used for system resource scheduling.

[0026] In step S120, based on the number of the original GHZ entangled states, multiple sets of original GHZ entangled states are generated, each set of original GHZ entangled states containing three mutually entangled particles.

[0027] It should be noted that the original GHZ entangled state is a three-particle maximally entangled state, where the three particles are mutually entangled, and a measurement of one particle instantaneously affects the states of the other two. This property forms the physical basis of quantum key distribution. Compared to EPR pairs, GHZ states simultaneously associate three particles, making it possible to generate a three-bit key for each entangled pair. Methods for generating GHZ states include linear optical methods, ion trap methods, or superconducting qubit methods.

[0028] The original GHZ entangled state is: in, The original GHZ entangled state, For the first particle to be in state, For the second particle to be in state, For the third particle to be in state, For the first particle to be in state, For the second particle to be in state, For the third particle to be in state.

[0029] In step S130, the first particle of the original GHZ entangled state of each group is assigned to the first particle sequence, the second particle is assigned to the second particle sequence, and the third particle is assigned to the third particle sequence.

[0030] It should be noted that during allocation, the three particles in each GHZ state are kept to have the same index number for subsequent pairing and entanglement recovery. Specifically, particles with the same index number in the first, second, and third particle sequences all come from the same original GHZ entangled state. This one-to-one index structure is maintained throughout all steps of the protocol; index misalignment will result in the final key failing to be generated correctly.

[0031] In step S140, the first particle sequence and the second particle sequence are distributed to the sender, and the third particle sequence is distributed to the receiver.

[0032] It should be noted that after distribution, the sender holds the first and second particle sequences, while the receiver holds the third particle sequence. All particles maintain their original entanglement. The distribution process is completed through quantum channels such as optical fibers or free space. Due to the noise and loss inherent in quantum channels, subsequent steps use quantum error-correcting codes to combat transmission errors.

[0033] In step S200, the sender applies a first unitary operation and a second unitary operation to each particle in the first particle sequence and the second particle sequence it holds, respectively, to obtain the operated first particle sequence and the operated second particle sequence, and forms a distinguishable GHZ entangled state with the third particle sequence.

[0034] It should be noted that the core step in encoding the key information is for the sender to apply unitary operations to its own first and second particle sequences. The first set of unitary operations contains four operations, and the second set contains two operations. Combinations of these two sets produce eight different unitary operation combinations. Each combination transforms the original GHZ state into a uniquely corresponding entangled state. This transformation process is measurement-independent and belongs to deterministic quantum operations. The mapping relationship between the output and input states is determined by the unitary operation matrix. Therefore, the sender only needs to select a combination of unitary operations to encode the three-bit key information into the GHZ state without sending any additional classical information to the receiver. Furthermore, the key information is determined by the output of the quantum random number generator, meaning the key will not be prematurely leaked due to false randomness.

[0035] Specifically, for the entangled state sequences K1, K2, and K3 distributed to Alice and Bob, we use K1(n), K2(n), and K3(n) to represent the nth particle in sequences K1, K2, and K3, respectively, where n = 1, 2, 3, ..., N. N is the number of GHZ states in the original GHZ state sequence; for example, if 10 GHZ states were initially distributed, then N = 10. To enable the entangled state particles distributed to Alice's side to generate more keys, Alice applies unitary operations to the two particles in each group. The unitary operations in sequence K1 are derived from... Choose from four unitary operations; the unitary operations in the K2 sequence are selected from... Choose between two operations.

[0036] After such unitary operations, mutually distinguishable quantum states emerge. This distinguishability allows the altered quantum states to transmit information, realizing the function of generating a 3-bit original key from a single GHZ entangled state. For N particle pairs in the K1 and K2 sequences, Alice needs to perform N two-quantum unitary operations to ensure that all GHZ states can generate the original key, as illustrated in the diagram below. Figure 4 As shown in the diagram. Different colors are used to represent different unitary operations, such as blue corresponding to... Operation, black corresponds to Operation, green corresponds to Operation, corresponding to red operate.

[0037] In one embodiment, such as Figure 5 As shown, step S200 may include the following sub-steps: In step S210, particles for which operations are applied are selected from the first unitary operation set to obtain the operated first particle sequence.

[0038] It should be noted that the first unitary operation set includes four types of operations, corresponding to the unit operation, bit flip operation, phase flip operation, and bit-phase joint flip operation, respectively. Different operations applied to the first particle sequence cause the entire three-particle system to evolve into different entangled states. In actual implementation, these operations are performed by placing specific single-qubit gates on the quantum circuit.

[0039] The first set of unitary operations includes: , , , ; Among them, among them, It is the identity matrix. The Pauli-X matrix, For the Pauli-Y matrix, The Pauli-Z matrix, The imaginary unit satisfies .

[0040] In step S220, particles for which operations are applied are selected from the second unitary operation set to obtain the operated second particle sequence.

[0041] It should be noted that the second unitary operation set contains two types of operations, corresponding to the unit operation and the bit flip operation, respectively, and its scope is limited to the second particle sequence; the four choices of the first unitary operation set and the two choices of the second unitary operation set combine to produce a total of eight different evolution results, corresponding to eight different entangled states.

[0042] The second set of unitary operations includes: , .

[0043] In step S230, the manipulated first particle sequence, the manipulated second particle sequence, and the third particle sequence are combined to form a distinguishable GHZ entangled state.

[0044] It should be noted that after the unitary operation, the first particle that has been operated, the second particle that has been operated, and the third particle that has not been operated together in each group constitute one of the eight mutually distinguishable GHZ entangled states. Each entangled state uniquely corresponds to a set of three-bit keys, with the correspondence ranging from all zeros to all ones. Each three-bit binary string corresponds to a specific entangled state. The eight states are orthogonal to each other and can be perfectly distinguished by subsequent GHZ basis measurements.

[0045] The distinguishable GHZ entangled states include: in, The first distinguishable GHZ entangled state, The second distinguishable GHZ entangled state, The third distinguishable GHZ entangled state, This is the fourth distinguishable GHZ entangled state. This is the fifth distinguishable GHZ entangled state. It is the sixth distinguishable GHZ entangled state. This is the seventh distinguishable GHZ entangled state. This is the eighth distinguishable GHZ entangled state.

[0046] In step S300, the sender randomly selects a Z-based or X-based to prepare multiple check particles, obtains a check sequence and a corresponding preparation base, and pairs each check particle in the check sequence with particles in the operated first particle sequence and particles in the operated second particle sequence to form multiple composite particle groups.

[0047] It should be noted that the verification sequence is used to detect the presence of eavesdropping or excessive noise in the quantum channel. The sender randomly selects either the Z-based or X-based basis to prepare verification particles, and the receiver, after decoding, selects the measurement basis in the same random manner to measure the verification particles. Since the sender pre-records the preparation basis for each verification particle, both parties can subsequently assess the channel security by publicly comparing the consistency between the measurement basis and the preparation basis. If there is no eavesdropping in the channel, the measurement results under the same basis should be completely consistent; if eavesdropping exists, the error rate under the same basis should reach at least 25%. This method does not require complex Bell inequality verification and is directly applicable to GHZ state systems.

[0048] Specifically, traditional entangled quantum key distribution (EPR) determines whether eavesdropping occurs during key distribution by detecting whether the EPR pairs satisfy Bell's inequality: when the CHSH (Clauser-Horne-Shimony-Holt inequality) correlation function value is greater than 2, it proves that the EPR pairs are intact and there is no eavesdropping; when the CHSH correlation function value is less than 2, it proves that the particles have reverted to the classical state, the entanglement is broken, and eavesdropping is determined to exist. However, such detection methods require complex operational steps and are not suitable for GHz entangled states. Therefore, this application proposes an eavesdropping detection method based on a verification sequence as follows: First, randomly select either the Z-based or X-based approach to prepare N check particles, assembling them into a check sequence P1. Let each particle in the sequence be P1(n), where n = 1, 2, 3, ..., N. The number of particles in the check sequence is N, just like the number of particles in sequences K1 and K2. They can be paired one-to-one, i.e., [K1(n), K2(n), P1(n)], n = 1, 2, 3, ..., N are grouped together. Under the random selection of the Z-based or X-based approach, the check sequence particles are... One of four states, with equal probability of occurrence. After sequences K1, K2, and P1 are transmitted to Bob, Bob randomly selects either the Z basis or the X basis as the measurement basis. Each particle in the P1 sequence corresponds to a measurement basis. If the measurement basis of a particle P1(i) matches the preparation basis chosen by Alice, then the group [K1(i), K2(i), P1(i)] can be used as the particle for subsequent key generation; if it does not match the preparation basis, the group [K1(i), K2(i), P1(i)] is discarded. If there is no eavesdropping during key distribution, the particle states in the P1 sequence should remain unchanged. When Alice's preparation basis is the same as Bob's measurement basis, Bob's measurement result has no error rate; if there is eavesdropping, the particle states in the P1 sequence will change. When Alice's preparation basis is the same as Bob's measurement basis, the measurement result will have an error rate greater than or equal to 25%. The presence of eavesdropping can be detected through the results obtained by simple quantum measurement operations. The calculation steps for the 25% error threshold are as follows: Alice randomly selects either the Z-based or X-based matrix with equal probability (50%) during preparation, and Bob randomly selects either the Z-based or X-based matrix with equal probability (50%) during measurement. Eve, the eavesdropper, will also randomly select either the Z-based or X-based matrix for measurement with equal probability (50%) even without prior information leakage, thus eavesdropping. Errors are only introduced when Alice's preparation matrix and Bob's measurement matrix are consistent, and Eve's chosen eavesdropping matrix is ​​different from both Alice's and Bob's. For example, if Alice chooses the X-based matrix for preparation, Eve uses the Z-based matrix for measurement to eavesdrop, and Bob selects the X-based matrix to measure the state of the verified particle after eavesdropping, the probability of measurement error is 50%. It is evident that the entire process does not necessarily introduce an error rate, and it is a conditional probability calculation. Definition What is the probability that both Alice and Bob choose the Z-basis? Let X be the probability that both Alice and Bob choose the X basis. The quantum bit error rate (QBER) can then be calculated. .

[0049] In one embodiment, such as Figure 6 As shown, step S300 may include the following sub-steps: In step S310, the sender randomly selects either a Z-basis or an X-basis as a preparation basis for each original GHZ entangled state, and randomly prepares a quantum state as a verification particle under the preparation basis; wherein each verification particle is located at... The probability of any of the four states is equal.

[0050] It should be noted that the four states include two states under the Z basis and two states under the X basis. Each state has a probability of one-quarter. The random selection of the preparation basis is used to prevent eavesdropping: if an eavesdropper intercepts the verification particle, he will not know the original preparation basis and will inevitably introduce errors at some positions. The preparation process is completed independently by the sender. The length of the verification sequence is equal to the number of entangled states in GHZ.

[0051] In step S320, all the verification particles are arranged in order to form a verification sequence, and the preparation base corresponding to each verification particle is recorded.

[0052] It should be noted that the preparation base sequence is kept secret by the sender and used only during subsequent public alignment; it must not be disclosed in advance. The check particles are arranged in the original order to form the check sequence, and their indices are aligned with the indices of the first and second particle sequences. The preparation base of each check particle is recorded for comparison with the receiver's measurement base after decoding.

[0053] In step S330, each check particle in the check sequence is paired one-to-one with a particle in the operated first particle sequence and a particle in the operated second particle sequence at the same position to form multiple composite particle groups; wherein, the composite particle group includes an operated first particle, an operated second particle and a check particle.

[0054] It should be noted that the formation of composite particle groups binds each check particle to a pair of operated particles, providing a unified index structure for subsequent encoding and eavesdropping detection. Each composite particle group contains three particles: an operated first particle, an operated second particle, and a check particle. This pairing method ensures that any interference with the key particle affects the corresponding check particle.

[0055] In step S400, the sender encodes each of the composite particle groups using quantum error correction codes to obtain the encoded composite quantum system, and then transmits the composite quantum system to the receiver.

[0056] It should be noted that the [[8,3,3]] Gottesman quantum error-correcting code encodes three logical bits (i.e., the three particles in the composite particle group) into eight physical bits with a code distance of 3, which can correct any single-bit error. When the encoded composite quantum system passes through a noisy channel, even if any physical bit flips or has a phase error, the receiver can still accurately identify and correct the error through the symptom extraction circuit, thereby recovering the original three logical bits. In addition, the encoding process creates entanglement among the three particles in the composite particle group, enhancing the sensitivity of eavesdropping detection. That is, interference from an eavesdropper on any particle will simultaneously affect the states of all three particles and be exposed through the check sequence.

[0057] Specifically, the [[8,3,3]] Gottesman quantum error-correcting code, as an early proposed stable subcode, has had its mathematical relationships and physical implementation fully proven and developed. Structurally, [[8,3,3]] represents a total of 8 physical bits, of which 3 are logic bits and 5 are auxiliary bits. The code distance is 3, and it can correct any error of 1 bit, including bit flip errors, phase flip errors, and combined errors. Its circuit is as follows: Figure 7 As shown, it consists of three circuit parts: encoder, symptom extraction and error correction, which are connected according to the stable subgenerator setup.

[0058] The particles in sequences K1, K2, and P1 are selected as the inputs to the circuit. The number of inputs, or encodings, is determined based on the number of particles N in sequences K1, K2, and P1. The encoded composite quantum system then possesses error-resistant capabilities, correcting potential one-bit quantum errors that may occur during transmission of particles in sequences K1, K2, and P1, thus improving the reliability of the method. Furthermore, the three particles in the encoded group [K1(i), K2(i), P1(i)] become entangled, meaning that interference from an eavesdropper can simultaneously affect all three particles. According to the eavesdropping detection method based on a verification sequence mentioned in step S300, any eavesdropping attempt by an eavesdropper on any one of the three particles can be detected through the verification sequence.

[0059] In one embodiment, such as Figure 8 As shown, step S400 may include the following sub-steps: In step S410, the three particles in each composite particle group are used as the three logical bits of the [[8,3,3]] Gottesman quantum error-correcting code as input, and five initialization bits are introduced for each composite particle group. Auxiliary bits of the state.

[0060] It should be noted that 5 states will be included in the encoding. The purpose of this particle is to map the original three logical bits into mutually orthogonal and distinguishable codeword spaces, making error detection easier. The error correction symptom extraction part will also incorporate five states. The purpose of these particles is to store symptom information.

[0061] In step S420, the three logical bits are encoded into an eight-physical-bit quantum state through the encoder circuit of the [[8,3,3]] Gottesman quantum error-correcting code.

[0062] It should be noted that the encoding process expands the information of three logical bits into a codeword space of eight physical bits, so that the final quantum state can resist errors of a single arbitrary bit, including bit flip errors, phase flip errors, and combinations of both.

[0063] In step S430, the eight-physical-bit composite quantum system obtained by encoding all composite particle groups is sent to the receiver through a quantum channel.

[0064] It should be noted that after encoding, the sender transmits the eight-physical-bit composite quantum system corresponding to all composite particle groups to the receiver one by one through the quantum channel. The quantum channel is subject to noise interference and eavesdropping risks. The encoded composite quantum system has error correction capabilities to improve transmission fidelity.

[0065] In step S500, the receiver decodes the composite quantum system using the quantum error correction code, randomly selects the comparison results between the measurement basis and the preparation basis, retains the particle group corresponding to the same position of the measurement basis and the preparation basis as the effective particle group, and performs GHZ basis measurement on the particles in the effective particle group corresponding to the same distinguishable GHZ entangled state to generate the final key.

[0066] It should be noted that the receiver first decodes and corrects the received eight-physical-qubit composite quantum system to recover the manipulated first particle sequence, the manipulated second particle sequence, and the verification sequence. Subsequently, the receiver discloses the measurement basis used to measure the verification sequence, and the sender discloses the preparation basis used to prepare the verification sequence. Both parties compare and retain the positions where the basis is the same. The manipulated first and second particles corresponding to these positions, together with the corresponding third particle held by the sender, constitute a complete GHZ entangled state. The receiver performs a GHZ basis measurement on this complete entangled state. This measurement basis consists of eight projection operators, each corresponding one-to-one with the eight entangled states encoded by the sender. The measurement result is directly mapped to a three-bit binary string. The final key is obtained by concatenating the binary strings of all valid positions in index order.

[0067] Specifically, such as Figure 9As shown, Bob initially receives a composite quantum state in the [[8,3,3]] Gottesman code encoding state, which requires a decoder to obtain the particle states in the original sequences K1, K2, and P1. Then, according to the method mentioned in step S300, the particles in the same group as the measurement basis and the preparation basis are retained, denoted as [K1(t), K2(t)], where the position numbers of the same positions in the preparation basis and the measurement basis are uniformly denoted as t. [K1(t), K2(t), K3(t)] belong to the GHZ entangled state, which was distributed to Alice and Bob in step S100, but the entanglement within it has not changed. Now, [K1(t), K2(t), K3(t)] is measured under the GHZ basis, which can distinguish the expressions of the projection operators of the 8 encoded states.

[0068] By measuring with the projection operator, Bob can determine which of the eight encoded states this GHZ entangled state is in, and thus decipher the information to generate a 3-bit key. This method is repeated until all sets [K1(t), K2(t), K3(t)] with the same preparation and measurement bases are measured, resulting in a complete quantum key, i.e., key distribution is complete.

[0069] In one embodiment, such as Figure 10 As shown, step S500 may include the following sub-steps: In step S510, the composite quantum system is decoded using the [[8,3,3]] Gottesman quantum error correction code to obtain the first manipulated particle sequence, the second manipulated particle sequence, and the verification sequence.

[0070] It should be noted that before decoding, the error symptoms are calculated by the symptom extraction circuit, and error correction is performed based on the symptoms to recover the original three logic bits. Since five auxiliary bits are introduced during symptom extraction and error correction, transmission errors are detected and corrected without destroying the logic bit information. After decoding, the receiver obtains estimates of the first manipulated particle sequence, the second manipulated particle sequence, and the check sequence.

[0071] In step S520, either Z-based or X-based is randomly selected as the measurement basis, and the selected measurement basis is compared with the preparation basis disclosed by the sender. The manipulated first particle and manipulated second particle corresponding to the same position of the measurement basis and the preparation basis are retained as the effective particle group.

[0072] It should be noted that during the comparison, the receiver discloses the base type (Z-based or X-based) used for each measurement, while the sender discloses the base type used to prepare each check particle. Both parties compare the base type at each position one by one. If the base types are the same, the particle set corresponding to that position is retained for subsequent key generation; if the base types are different, the particle set corresponding to that position is discarded. If eavesdropping occurs, the error rate at positions with the same base type increases significantly.

[0073] In step S530, the manipulated first particle and manipulated second particle retained at each effective position in the effective particle group are combined with the third particle at the same position in the third particle sequence to obtain a complete GHZ entangled state; the complete GHZ entangled state belongs to the distinguishable GHZ entangled state.

[0074] It should be noted that the three particles of the original GHZ entangled state are assigned to the sender and receiver respectively in the first step of the protocol, and the receiver does not perform any operation on the third particle sequence during transmission. Therefore, the third particle maintains its original entanglement relationship with the operated first and second particles. The retained particles at the same index position are recombine to recover the complete GHZ entangled state.

[0075] In step S540, a GHZ basis measurement is performed on the complete GHZ entangled state, and the measurement result is directly mapped to a set of three-bit binary strings.

[0076] It should be noted that the GHZ basis consists of eight projection operators, each of which corresponds to a distinguishable GHZ entangled state. When performing GHZ basis measurements on a complete GHZ entangled state, the quantum state of the system collapses into the subspace corresponding to one of the projection operators. The measurement result directly gives the three-bit binary string corresponding to the entangled state without any additional decoding steps.

[0077] The projection operator for the GHZ-based measurement includes: in, For the first projection operator, For the second projection operator, For the third projection operator, For the fourth projection operator, For the fifth projection operator, For the sixth projection operator, For the seventh projection operator, For the eighth projection operator, ; To retain only the quantum state Projection operator of components, The first coherent cross term describes arrive quantum coherence, for The first Hermitian conjugate of is the first anticoherent term. To retain only the quantum state Projection operator for components; To retain only the quantum state Projection operator of components, The second coherent cross term describes arrive quantum coherence, for The second Hermitian conjugate is the second anticoherent term. To retain only quantum states Projection operator for the middle component; To retain only the quantum state Projection operator of components, The third coherent cross term describes arrive quantum coherence, for The third Hermitian conjugate is the third anticoherent term. To retain only the quantum state Projection operator for components; To retain only the quantum state Projection operator of components, The fourth coherent cross term describes arrive quantum coherence, for The fourth Hermitian conjugate is the fourth anticoherent term. To retain only the quantum state Projection operator for components.

[0078] In step S550, the three-bit binary strings corresponding to all valid positions are concatenated in sequence to form the final key.

[0079] It should be noted that the splicing is performed in ascending order of the original indices of the valid positions, meaning the retained particle groups are arranged according to their order of appearance in the sequence; the final binary string is the quantum key shared by the sender and receiver. If the error rate exceeds a preset threshold, such as 25%, during the verification step, it indicates that eavesdropping may have occurred during communication, and both parties discard all generated data and restart the key distribution process.

[0080] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. An efficient quantum key generation method based on entangled states and stable subcodes, characterized in that, include: The sender constructs multiple sets of original GHZ entangled states, assigns the three particles in each set of original GHZ entangled states to the first particle sequence, the second particle sequence, and the third particle sequence, respectively, and distributes the first particle sequence and the second particle sequence to the sender, and the third particle sequence to the receiver; The sender applies a first unitary operation and a second unitary operation to each particle in the first particle sequence and the second particle sequence it holds, respectively, to obtain the operated first particle sequence and the operated second particle sequence, and forms a distinguishable GHZ entangled state with the third particle sequence. The sender randomly selects Z-based or X-based to prepare multiple check particles, obtains a check sequence and the corresponding preparation base, and pairs each check particle in the check sequence with the particles in the operated first particle sequence and the particles in the operated second particle sequence to form multiple composite particle groups; The sender encodes each of the composite particle groups using quantum error correction codes to obtain the encoded composite quantum system, and then transmits the composite quantum system to the receiver. The receiver decodes the composite quantum system using the quantum error correction code, randomly selects the comparison results between the measurement basis and the preparation basis, retains the particle group corresponding to the same position of the measurement basis and the preparation basis as the effective particle group, and performs GHZ basis measurement on the particles in the effective particle group corresponding to the same distinguishable GHZ entangled state to generate the final key.

2. The efficient quantum key generation method based on entangled states and stable subcodes according to claim 1, characterized in that, The steps of constructing multiple sets of original GHZ entangled states by the sender, assigning the three particles in each set of original GHZ entangled states to a first particle sequence, a second particle sequence, and a third particle sequence, and distributing the first particle sequence and the second particle sequence to the sender, and distributing the third particle sequence to the receiver, include: Based on the final key length to be generated, determine the required number of GHZ entangled states, which are used as the original GHZ entangled states; wherein, the number of the original GHZ entangled states is greater than the final key length; Based on the number of the original GHZ entangled states, multiple sets of original GHZ entangled states are generated, each set of original GHZ entangled states containing three mutually entangled particles; The first particle of the original GHZ entangled state in each group is assigned to the first particle sequence, the second particle to the second particle sequence, and the third particle to the third particle sequence; The first particle sequence and the second particle sequence are distributed to the sender, and the third particle sequence is distributed to the receiver.

3. The efficient quantum key generation method based on entangled states and stable subcodes according to claim 2, characterized in that, The original GHZ entangled state is: in, The original GHZ entangled state, For the first particle to be in state, For the second particle to be in state, For the third particle to be in state, For the first particle to be in state, For the second particle to be in state, For the third particle to be in state.

4. The efficient quantum key generation method based on entangled states and stable subcodes according to claim 1, characterized in that, The step of the sender applying a first unitary operation and a second unitary operation to each particle in its first particle sequence and second particle sequence, respectively, to obtain the operated first particle sequence and the operated second particle sequence, and forming a distinguishable GHZ entangled state with the third particle sequence, includes: Select the particles from the first set of unitary operations to which the operation is applied in the first particle sequence to obtain the first sequence of operated particles; Select particles from the second set of unitary operations to be operated on in the second particle sequence to obtain the operated second particle sequence; The manipulated first particle sequence, the manipulated second particle sequence, and the third particle sequence are combined to form a distinguishable GHZ entangled state.

5. The efficient quantum key generation method based on entangled states and stable subcodes according to claim 4, characterized in that, The first set of unitary operations includes: ， ， ， ； in, It is the identity matrix. The Pauli-X matrix, For the Pauli-Y matrix, The Pauli-Z matrix, The imaginary unit; The second set of unitary operations includes: ， 。 6. The efficient quantum key generation method based on entangled states and stable subcodes according to claim 4, characterized in that, The distinguishable GHZ entangled states include: in, The first distinguishable GHZ entangled state, The second distinguishable GHZ entangled state, The third distinguishable GHZ entangled state, This is the fourth distinguishable GHZ entangled state. This is the fifth distinguishable GHZ entangled state. It is the sixth distinguishable GHZ entangled state. This is the seventh distinguishable GHZ entangled state. This is the eighth distinguishable GHZ entangled state.

7. The efficient quantum key generation method based on entangled states and stable subcodes according to claim 1, characterized in that, The step of the sender randomly selecting a Z-based or X-based basis to prepare multiple check particles, obtaining a check sequence and a corresponding preparation basis, and pairing each check particle in the check sequence with particles in the manipulated first particle sequence and the manipulated second particle sequence to form multiple composite particle groups includes: The sender randomly selects either a Z-based or an X-based basis as the preparation basis for each original GHZ entangled state, and randomly prepares a quantum state as a verification particle under the preparation basis; wherein each verification particle is located at... The probability of one of the four states is equal; All the test particles are arranged in order to form a test sequence, and the preparation substrate corresponding to each test particle is recorded; Each check particle in the check sequence is paired one-to-one with a particle in the operated first particle sequence and a particle in the operated second particle sequence at the same position to form multiple composite particle groups; wherein, the composite particle group contains an operated first particle, an operated second particle and a check particle.

8. The efficient quantum key generation method based on entangled states and stable subcodes according to claim 1, characterized in that, The step of the sender encoding each of the composite particle groups using quantum error correction codes to obtain an encoded composite quantum system and transmitting the composite quantum system to the receiver includes: The three particles in each composite particle group are used as the three logical bits of the [[8,3,3]] Gottesman quantum error-correcting code as input, and five initializations are introduced for each composite particle group. Auxiliary bits of the state; The encoder circuit of the [[8,3,3]] Gottesman quantum error-correcting code encodes the three logical bits into an eight-physical-bit quantum state; The eight-physical-bit composite quantum system obtained by encoding all composite particle groups is sent to the receiver via a quantum channel.

9. The efficient quantum key generation method based on entangled states and stable subcodes according to claim 1, characterized in that, The receiver decodes the composite quantum system using the quantum error-correcting code, randomly selects the comparison results between the measurement basis and the preparation basis, retains the particle groups corresponding to the same positions in the measurement basis and the preparation basis as valid particle groups, and performs GHZ basis measurements on the particles corresponding to the same distinguishable GHZ entangled state in the valid particle groups to generate the final key. The steps include: The composite quantum system is decoded using the [[8,3,3]] Gottesman quantum error correction code to obtain the first manipulated particle sequence, the second manipulated particle sequence, and the verification sequence; Randomly select Z-based or X-based as the measurement basis, and compare the selected measurement basis with the preparation basis disclosed by the sender. Retain the operated first particle and operated second particle corresponding to the same position of the measurement basis and the preparation basis as the effective particle group. The manipulated first particle and manipulated second particle retained at each effective position in the effective particle group are combined with the third particle at the same position in the third particle sequence to obtain a complete GHZ entangled state; the complete GHZ entangled state belongs to the distinguishable GHZ entangled state; Perform GHZ basis measurements on the complete GHZ entangled state and directly map the measurement results to a set of three-bit binary strings; Concatenate the three-bit binary strings corresponding to all valid positions in order to form the final key.

10. The efficient quantum key generation method based on entangled states and stable subcodes according to claim 9, characterized in that, The projection operator for the GHZ-based measurement includes: in, For the first projection operator, For the second projection operator, For the third projection operator, For the fourth projection operator, For the fifth projection operator, For the sixth projection operator, For the seventh projection operator, This is the eighth projection operator; To retain only the quantum state Projection operator of components, The first coherent cross term describes arrive quantum coherence, for The first Hermitian conjugate of is the first anticoherent term. To retain only the quantum state Projection operator for components; To retain only the quantum state Projection operator of components, The second coherent cross term describes arrive quantum coherence, for The second Hermitian conjugate is the second anticoherent term. To retain only quantum states Projection operator for the middle component; To retain only the quantum state Projection operator of components, The third coherent cross term describes arrive quantum coherence, for The third Hermitian conjugate is the third anticoherent term. To retain only the quantum state Projection operator for components; To retain only the quantum state Projection operator of components, The fourth coherent cross term describes arrive quantum coherence, for The fourth Hermitian conjugate is the fourth anticoherent term. To retain only the quantum state Projection operator for components.

Images