CN112367167A - Quantum secret sharing method and system based on tensor network state dynamic compression - Google Patents

Quantum secret sharing method and system based on tensor network state dynamic compression Download PDF

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CN112367167A
CN112367167A CN202011168665.5A CN202011168665A CN112367167A CN 112367167 A CN112367167 A CN 112367167A CN 202011168665 A CN202011168665 A CN 202011168665A CN 112367167 A CN112367167 A CN 112367167A
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CN112367167B (en
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赖红
张强
刘紫豪
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Southwest University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/085—Secret sharing or secret splitting, e.g. threshold schemes

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Abstract

The invention discloses a quantum secret sharing method and a quantum secret sharing system based on tensor network state dynamic compression, wherein the method comprises the following steps: s1: the distributor carries out local equidistant transformation on the quantum state secret information to be shared according to the form of matrix product state, and decomposes the quantum state secret information into corresponding secret shares according to the number of participants; s2: the distributor distributes the decomposed secret shares to corresponding participants; s3: the participants mutually share the secret share obtained by the participants; s4: the participants who obtain all secret shares acquire the process information of local equidistant transformation from the distributor, and the shared quantum state secret information is restored by combining and decompressing. The effect is as follows: all classical and quantum participants can use quantum bits with higher quantity indexes than those received by the classical and quantum participants to decompress the state, so that the method has obvious storage advantages, improves the efficiency and precision of quantum communication, and greatly reduces the size of a quantum memory.

Description

Quantum secret sharing method and system based on tensor network state dynamic compression
Technical Field
The invention relates to a quantum communication technology, in particular to a quantum secret sharing method and system based on tensor network state dynamic compression.
Background
It is well known that for a classical system, the amount of information that can be extracted must be the same as the amount of information needed to accurately describe the state of the system. This is not the case for a quantum system. The amount of information required to fully describe the state of a qubit is infinite, but no more than 1 bit of information can be extracted by measuring the quantum state. This essential difference between quantum systems and classical systems provides the possibility for new types of data compression that do not require classical simulation. In quantum mechanics, exponential storage is enabled, although all the information contained in a system set cannot be compressed into a single quantum copy. Worse still, measurement of quantum states is expensive for quantum-mechanical-based quantum communication such as quantum secret sharing and quantum key distribution. Because quantum states are difficult to prepare and to some extent, each measurement will cause the quantum state to collapse or be disturbed. Therefore, quantum communication is extremely challenging in practical applications.
Recently, many researchers have shown great interest in quantum multimers and have made significant progress. However, the quantum multimodality approach has not been applied to quantum state secret sharing. It should be noted that if we simply replace the secret sharing state with a quantum multi-volume state with a small number of quantum bits, the corresponding hilbert space grows exponentially, making secret sharing difficult to handle. Therefore, it is important and pressing to develop compression algorithms to reduce the exponential growth of the system.
Fortunately, tensor network states (mainly including Matrix Product State (MPS), Tree Tensor Network (TTN), Projection Entanglement Pairwise State (PEPS), and multi-scale entanglement reformulation trial state (MERA)) have been proposed to solve this problem. Tensor network states are considered as the most promising tools for describing quantum-multi-body systems, and reference can be made to the following documents:
[1]Chabuda,K.,Dziarmaga,J.,Osborne,T.J.,&Demkowicz-Dobrzaski,R.Tensor-network approach for quantum metrology in many-body quantum systems.Nature Communications,11(1),1-12(2020).
[2]Ran,S.J.,Piga,A.,Peng,C.,Su,G.,&Lewenstein,M.Few-body systems capture many-body physics:Tensor network approach.Physical Review B,96(15),155120(2017).
tensor networks are connected by tensor contraction, represented by a pattern of wire connections (circles, squares, ellipses, diamonds, or triangles). Tensor networks provide highly accurate encoding of relevant quantum properties, such as quantum entanglement. The state of a quantum multi-body system can be represented mathematically. More importantly, tensor networks have significant computational advantages derived from the fact that: tensor networks can approximate a complex quantum state with a simpler structure. In essence, tensor networks can be viewed as a data compression protocol, preserving only those properties that are sufficient to describe the behavior of quantum states. The compression operation can significantly reduce the increase in computational complexity. This implies a strategy for efficient management of resources to obtain quantum states with as high a fidelity as possible. However, existing quantum state secret sharing schemes do not use quantum state compression.
Disclosure of Invention
In view of the above, the present invention firstly provides a quantum secret sharing method based on tensor network state dynamic compression, which fully utilizes the idea of compressing the tensor network state, and the technical means of compressing the tensor network state is particularly useful when a secret sharing memory is difficult to obtain or expensive in cost, and can greatly compress required data, thereby improving information transmission efficiency.
In order to achieve the purpose, the invention adopts the following specific technical scheme:
a quantum secret sharing method based on tensor network state dynamic compression is characterized by comprising the following steps:
s1: the distributor carries out local equidistant transformation on the quantum state secret information to be shared according to the form of matrix product state, and decomposes the quantum state secret information into corresponding secret shares according to the number of participants;
s2: the distributor distributes the decomposed secret shares to corresponding participants, wherein one part of the participants are obtained through a quantum channel, and the other part of the participants are obtained through a classical channel;
s3: the participants mutually share the secret share obtained by the participants;
s4: the participants who obtain all secret shares acquire the process information of local equidistant transformation from the distributor, and the shared quantum state secret information is restored by combining and decompressing.
Alternatively, when the number of participants is 2, secret shares depending on the tensor of the parameter are allocated to the first participant through the quantum channel, and secret shares depending on the tensor of the constant are allocated to the second participant through the classical channel.
Optionally, after l rounds of local equidistant transformation in step S1, the quantum state secret information is compressed as:
Figure BDA0002746577210000031
wherein:
Figure BDA0002746577210000032
representing the matrix product state obtained after the first round of local equidistant transformation, with the maximum value of
Figure BDA0002746577210000033
< L and | R > are secret shares that depend on the tensor of the parameter;
Figure BDA0002746577210000034
secret shares that are constants dependent tensors;
n is the number of systems and is a power of 2; i1>Process information representing a local equidistant transformation; i.e. i1＝1～dp,dpRepresenting the dimensions of the system.
Optionally, the respective secret shares are decomposed into block tensors according to the dimensions of the tensors and distributed to the corresponding participants.
Alternatively, the matrix product state of the quantum state secret information shared in step S1 is dynamically generated in a stream manner, and when a new matrix product state is added, the following steps are performed:
s101: converting the initial matrix product state and the newly added matrix product state into corresponding tensors;
s102: respectively executing zero filling operation on the tensors to enable the zero filling operation and the tensors to have the same order and dimension, so that a zero filling tensor is obtained;
s103: and adding the two zero-filling tensors to obtain an updated matrix product state.
Based on the method, the invention also provides a tensor network state-based dynamic compression quantum secret sharing system which adopts the quantum secret sharing method to carry out quantum secret sharing so as to realize quantum signature, quantum authentication or quantum key distribution.
The invention has the technical effects that:
the invention provides a compression method for general family states with limited local or global storage resources, which can compress the states into an O (logn) quantum bit memory without errors. All classical and quantum participants can decompress the state by using quantum bits with a higher number index than the number index received by the classical and quantum participants, and the method has obvious storage advantages and improves the efficiency and the precision of quantum communication. Furthermore, it greatly reduces the size of the quantum memory, since data compression stores all available information for quantum states in fewer physical qubits.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a schematic analysis diagram of equidistant output as matrix product states;
FIG. 2 is a schematic analysis diagram of the output state represented as the matrix product state;
FIG. 3 is a schematic diagram of a process for iteratively performing quantum secret compression using a local area compression protocol;
FIG. 4 is a flow chart of a method of the present invention;
FIG. 5 is a diagram illustrating the relationship between matrix product states and their corresponding tensors;
FIG. 6 is a diagram illustrating a process of updating the product state of the shared matrix.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments, it being understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
First, we present some basic definitions to facilitate a basic understanding of the concepts involved in the subsequent processing, where:
the Matrix Product State (MPS) is specifically defined as:
Figure BDA0002746577210000051
after simplification, the following relationships are present:
Figure BDA0002746577210000052
the equidistant distance is defined as:
if it is satisfied with
Figure BDA0002746577210000053
Or
Figure BDA0002746577210000054
Scale d1×d2The matrix M of (a) is equidistant. d1And d2The dimensions of the matrix M are represented by,
Figure BDA0002746577210000055
representing the conjugate transition rank of the matrix M;
and the definition of local equidistant is:
let H and G be both Hilbert spaces, and T be a bounded linear operator from H to G. If T is equidistant in subspace M of H, at M⊥Above 0, T is the local equidistant operator with M as the initial space and N ═ TM as the final space. If and only if
Figure BDA0002746577210000056
And
Figure BDA0002746577210000057
when the orthogonal projection operators are respectively on M and N, T is a local equidistant operator taking M as an initial space and N as a final space.
For example, the following two relationships:
Figure BDA0002746577210000061
Figure BDA0002746577210000062
obviously, set up
Figure BDA0002746577210000063
When in use
Figure BDA0002746577210000064
Replace the first I2Then, the following equation is also true:
Figure BDA0002746577210000065
and the definition of the local area compression protocol is:
given a composite system
Figure BDA0002746577210000066
Pure state of (1)
Figure BDA0002746577210000067
It comprises a physical system P (Hilbert space is H)P) And environment E (Hilbert space H)E). The local area compression protocol can be equidistant from local area V HP→HMTo construct, the local equidistant V satisfies the following equation:
Figure BDA0002746577210000068
wherein IEIs the unit operator on system E.
As shown in fig. 1, equidistant V(1)Is itself an MPS, where dcRepresents the key dimension, dpRepresenting physical dimensions, and, local equidistant Vi,i+1The local area compression protocol mentioned by the above formula is satisfied, specifically:
Figure BDA0002746577210000071
wherein
Figure BDA0002746577210000072
Is the unit operator for all systems except the i-th and i + 1-th systems.
Likewise, for arbitrary | L>And | R>To make a local area equidistant V1,2,V3,4,…,Vn-1,nActing at | ΨL,R>Above, the following relationship can be obtained:
Figure BDA0002746577210000073
meaning that the product is equidistant
Figure BDA0002746577210000074
An exact compression protocol is defined, the initial n systems (dimensions are d)p) Can be reduced to n/2 systems (dimensions are all
Figure BDA0002746577210000075
) The specific process is shown in fig. 2.
As can be seen from FIG. 2, the output states
Figure BDA0002746577210000076
Can be expressed as MPS form, | L>And | R>Referred to as a boundary condition, is HcTwo vectors in (1).
In FIG. 2, the output states
Figure BDA0002746577210000077
Can be expressed in MPS form. More importantly, because of the equidistant V(1)The output of (c) is itself also an MPS, so the structure can be iterated, as shown in fig. 3 in particular.
The main idea of the invention is to perform local compression on each pair of adjacent physical systems and iterate the compression protocol until a smaller memory size is not available, as shown in particular in fig. 3, so that the secret sharing scheme enables a reduction of memory, which may lead to higher efficiency and better performance under certain parameters. Therefore, we have devised an efficient scheme that allows sharing of a large quantum data.
Specifically, as shown in fig. 4, the present embodiment is illustrated by 2 participants:
in this scheme, it is assumed that there is a secret distributor, a quantum participant Alice and a classical participant Bob. The goal is to share MPS | ΨL,R>Where Alice holds the secret share of the tensor (which depends on the parameters) and Bob also holds the secret share of the tensor (which depends on the constant), i.e. | ΨL,R>＝{|ΨL,R>parameters}∪{|ΨL,R>constant}. Complete multi-modality | ΨL,R>Can be efficiently compressed and can be scaled from a fraction of { | ΨL,R>parametersAnd { | ΨL,R>constantPrecise reconstruction (see fig. 4). Further, assume that Alice and Bob are paired with a key dimension d, except that the shared MPS is known to be location independentcAnd physical dimension dPNothing is known. For simplicity of representation, it is assumed that the number n of physical systems is a power of 2, i.e., n is 2l。
As can be seen from fig. 4, the quantum secret sharing method based on tensor network state dynamic compression provided by this embodiment includes the following steps:
s1: the distributor carries out local equidistant transformation on the quantum state secret information to be shared according to the form of matrix product state, and decomposes the quantum state secret information into corresponding secret shares according to the number of participants;
the distributor performs local area compression locally, iteratively, on each pair of adjacent physical systems that require a shared MPS. When there is no content to compress, the process ends;
distributor using local equidistant Vi,i+1(i ═ 1,2, …, n-1) to compress MPS | ΨL,R>As follows:
Figure BDA0002746577210000081
wherein
Figure BDA0002746577210000082
Is the unit operator of all systems except the i-th and i + 1-th systems;
according to the formula, for the first iteration, the requirement that the local equidistance is V is met1,2,V3,4,…,Vn-1,nThe distributor performs the following operations:
Figure BDA0002746577210000083
this condition means product equi-distance
Figure BDA0002746577210000084
An exact compression protocol is defined, i.e. n systems (all dimensions are d)p) Store to n/2 systems (all dimensions are
Figure BDA0002746577210000085
) In (1). At the same time, output state
Figure BDA0002746577210000086
Can be expressed in MPS form:
Figure BDA0002746577210000087
for the second iteration, the requirement that the local equidistance is V1,n/2,Vn/2+1,nThe distributor performs the following operations:
Figure BDA0002746577210000091
4 particles can be seen
Figure BDA0002746577210000092
Is faithfully encoded into a 2-particle state
Figure BDA0002746577210000093
Figure BDA0002746577210000094
Output state
Figure BDA0002746577210000095
Can be expressed in MPS form:
Figure BDA0002746577210000096
for the last iteration that satisfies the local compression condition in the above equation, the distributor performs the following operations:
Figure BDA0002746577210000097
it can be seen that 2 particles
Figure BDA0002746577210000098
Is faithfully encoded into a 1-particle state
Figure BDA0002746577210000099
V(l):＝V1,n. Output state
Figure BDA00027465772100000910
Can be expressed in MPS form:
Figure BDA00027465772100000911
therefore, { | ΨL,R>parameterIs composed of<L and R>Composition { | ΨL,R>constantIs composed of
Figure BDA00027465772100000912
The components of the composition are as follows,<l and R>Secret shares that are parameter dependent tensors;
Figure BDA00027465772100000913
secret shares that are constants dependent tensors; n is the number of the systems; i1>Process information representing a local equidistant transformation; i.e. i1＝1～dp,dpRepresenting the dimensions of the system.
S2: the distributor distributes the decomposed secret shares to corresponding participants, wherein one part of the participants are obtained through a quantum channel, and the other part of the participants are obtained through a classical channel;
in this example the number of participants is 2, so the system will depend on the secret share of the tensor of the parameter<L and R>(i.e., { | Ψ)L,R>parameter}) is assigned to the first participant Alice via a quantum channel, the security of which is guaranteed by the uncertainty principle and the unclonable theorem of the quantum states, secret shares that will depend on the tensor of the constant
Figure BDA00027465772100000914
Corresponding to the second participant Bob through a classical channel allocation. It should be noted that it is preferable that,
Figure BDA00027465772100000915
is a very small data and is not costly to transmit in a secure manner.
S3: the participants mutually share the secret share obtained by the participants;
s4: the participants who obtain all secret shares acquire the process information of local equidistant transformation from the distributor, and the shared quantum state secret information is restored by combining and decompressing.
Further obtaining information I from the distributorE(i.e. I)2,3,…,n-1) Then, according to the formula:
Figure BDA0002746577210000101
at some point, Alice or Bob may be selected to recover MPS | ΨL,R>
In the process of secret sharing, it may be necessary to add new participants, and the method proposed by the present invention is also very easy to adapt to the number change of participants, since MPS can be converted into tensor, so all dimensions of tensor can be divided into blocks. That is, the tensor can be divided into n smaller cell or block tensors as shown in fig. 5. The MPS state is converted into a corresponding tensor x, the tensor x is divided into block tensors, and finally compressed and distributed to the participants through steps S1-S4. At the same time, the original participants may also need to be deleted, but all dimensions of the tensor can be added to the larger block tensor, so that the tensor can be combined into m larger units according to the number of the remaining participants. That is, our solution can easily cope with changes in the number of participants.
Besides, the system also involves the problem of MPS update and sharing, the matrix product state of the quantum state secret information shared in step S1 is dynamically generated in a streaming manner, and when a new matrix product state is added, the following steps are performed:
s101: converting the initial matrix product state and the newly added matrix product state into corresponding tensors;
s102: respectively executing zero filling operation on the tensors to enable the zero filling operation and the tensors to have the same order and dimension, so that a zero filling tensor is obtained;
s103: and adding the two zero-filling tensors to obtain an updated matrix product state.
The above specific process can be seen from fig. 6, where X/Y represents the initial/new MPS and its corresponding tensor;
in combination with the description of the foregoing method, this embodiment further provides a quantum secret sharing system dynamically compressed based on a tensor network state, where quantum secret sharing is performed by using the quantum secret sharing method described above, so that quantum signature, quantum authentication, or quantum key distribution can be implemented.
To better understand the significance of this solution, the performance of the method and system proposed by the present invention is next analyzed:
(1) compression characteristics
For quantum state secret sharing scheme based on location-independent MPS of variable boundary conditions, we pair each pair of adjacent dcThe dimensional MPS uses local equidistant V1,2,V3,4,…,Vn-1,nN particle | ΨL,R>Faithfully compressed to n/2 particles
Figure BDA0002746577210000111
Then, using local equidistant V1,4,V5,8,…,Vn-3,nN/2 particle
Figure BDA0002746577210000112
Compressed into n/4 particles
Figure BDA0002746577210000113
n particle | ΨL,R>After log (n) iterations, the bit can be finally compressed
Figure BDA0002746577210000114
Qubits. Thus, the compression operation can be implemented by a quantum circuit with a depth of o (logn). Since the size of each local equidistance does not exceed the size of each local equidistance
Figure BDA0002746577210000115
And the quantum circuit uses n-1 such local equi-distances in total, the overall complexity of the encoding operation is O (poly (n)) (assuming dcIs a polynomial of n) which means that the compression is efficient in the number of physical systems. The same discussion applies to the decompression circuit, which can be obtained by inverting each gate of the encoding circuit. Note that the above-described techniqueCan also be used for local compression of MPS. It corresponds to a scenario where only a subset of the physical system has access to it.
It is believed that the above compression will become a reality in the future. It allows quantum state secret sharing for a small number of participants with limited storage capacity. Our compression method has many advantages over the prior art.
(2) Transmission characteristic
The application of a position independent MPS of variable boundary conditions gives our solution the transmission properties. In other words, our scheme can apply compression when local or global storage resources are limited. Tensor addition and subtraction shifts the large scale system to the smaller scale system with fewer participants. This is a feature and advantage not available with other quantum secret sharing schemes.
(3) Dynamic characteristics
We have great enthusiasm for designing quantum state secret sharing with limited storage capacity (or few participants), which enables our scheme to dynamically allow participants to join (register) or leave (deregister). There are two aspects to the dynamics, elastic compression and addition and subtraction of the tensor. For elastic compression, more storage capacity is needed when a new participant joins. In this case, the distributor appropriately reduces the number of compressions. For example, in distributing quantum secret shares, the distributor can replace equation (10) with equation (9). When the participant exits, the storage capacity decreases and the distributor can increase the number of compressions appropriately. For example, in distributing quantum secret shares, the distributor can replace equation (7) with equation (9).
For tensor addition and subtraction, our scheme can dynamically change the number of compressions depending on the storage capacity of the participant. This can be achieved by dividing the tensor and updating the MPS.
(4) Security analysis
Here we present a compression based
Figure BDA0002746577210000121
Security analysis of quantum multi-modal secret sharing. Based on<L and R>The secret is secure under the assumption that Alice cannot be intercepted or replaced during transmission without knowing it. Is not aware of<L and R>It is not possible for an eavesdropper Eve to simply follow
Figure BDA0002746577210000122
Middle recovery
Figure BDA0002746577210000123
While the distributor is transmitting
Figure BDA0002746577210000124
Is/are as follows<L and R>In time, Eve has the potential to intercept the entire communication and obtain the information sent to Alice<L and R>. Worse, Eve might pass the same intercepted by her<L and R>And her new MPS to mask her presence. However, if the transport state is highly entangled, Eve's interception attack can be detected. It is well known that the security of "standard" quantum state secret sharing depends on either non-locality or entanglement of the active sharing parties.
Because the compressed state is entangled, Alice can use an entanglement witness to measure and detect such entanglement. More importantly, the scholars indicate that anyone who wants to measure the multi-body bell associations can be detected. If Eve intercepts the quantum communication, she needs to resend to Alice the MPS with the same entanglement properties, which are neither too weak nor too strong. Thus, Eve can replace them with something completely unrelated. Interception can be detected when Alice performs the same measurements on these unrelated copies.
Note that the distributor does not allow Alice and Bob to obtain the key dimension dcAnd physical dimension dPHe can ensure that he is only the provider of MPS himself. Since the shared quantum states are designed in the form of MPS, the distributor can avoid sending polynomial-rich quantum states to resist quantum state chromatography attacks. In addition, Alice sends a small portion of classical information
Figure BDA0002746577210000131
To Bob, in this caseTransmitted over classical channels
Figure BDA0002746577210000132
Is/are as follows
Figure BDA0002746577210000133
The information of (a) is unnecessary.
In summary, the quantum secret sharing method and system provided by the present invention provide a compression means for the general family state with limited local or global storage resources, and the method can compress the state into the memory of o (logn) quantum bits without error. All classical and quantum participants can decompress the state with exponentially higher number of qubits than they receive. We have found that the location independent tensor network state (SITNS) approach provides a storage advantage. This improves the efficiency of quantum communication, improves the performance of certain parameters, and improves the accuracy of quantum communication. Furthermore, it greatly reduces the size of the quantum memory, since data compression stores all available information for quantum states in fewer physical qubits.
Our approach paves the way for handling big data secret state sharing through sub-polytopes. Furthermore, dynamic compressed quantum state secret sharing based on location-independent MPS can be generalized to location-independent PEPS defined on a square lattice.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which is stored in a storage medium (such as ROM/RAM, magnetic disk, optical disk) and includes instructions for enabling a terminal (such as a mobile phone, a computer, a server, or a network device) to execute the method according to the embodiments of the present invention.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (6)

1. A quantum secret sharing method based on tensor network state dynamic compression is characterized by comprising the following steps:
s1: the distributor carries out local equidistant transformation on the quantum state secret information to be shared according to the form of matrix product state, and decomposes the quantum state secret information into corresponding secret shares according to the number of participants;
s2: the distributor distributes the decomposed secret shares to corresponding participants, wherein one part of the participants are obtained through a quantum channel, and the other part of the participants are obtained through a classical channel;
s3: the participants mutually share the secret share obtained by the participants;
s4: the participants who obtain all secret shares acquire the process information of local equidistant transformation from the distributor, and the shared quantum state secret information is restored by combining and decompressing.
2. The quantum secret sharing method based on tensor network state dynamic compression as claimed in claim 1, wherein: when the number of participants is 2, secret shares depending on the tensor of the parameter are allocated to the first participant through the quantum channel, and secret shares depending on the tensor of the constant are allocated to the second participant through the classical channel.
3. The quantum secret sharing method based on tensor network state dynamic compression as claimed in claim 1 or 2, wherein: after l rounds of local equidistant transformation in step S1, the quantum state secret information is compressed as:
Figure FDA0002746577200000011
wherein:
Figure FDA0002746577200000012
representing the matrix product state obtained after the first round of local equidistant transformation, with the maximum value of
Figure FDA0002746577200000013
< L and | R > are secret shares that depend on the tensor of the parameter;
Figure FDA0002746577200000014
secret shares that are constants dependent tensors;
n is the number of systems and is a power of 2; i1>Process information representing a local equidistant transformation; i.e. i1＝1～dp,dpRepresenting the dimensions of the system.
4. The quantum secret sharing method based on tensor network state dynamic compression as claimed in claim 3, wherein: the respective secret shares are decomposed into block tensors according to the dimensions of the tensors and distributed to the corresponding participants.
5. The quantum secret sharing method based on tensor network state dynamic compression as claimed in claim 1 or 2, wherein: the matrix product state of the quantum state secret information shared in step S1 is dynamically generated in a streaming manner, and when a new matrix product state is added, the following steps are performed:
s101: converting the initial matrix product state and the newly added matrix product state into corresponding tensors;
s102: respectively executing zero filling operation on the tensors to enable the zero filling operation and the tensors to have the same order and dimension, so that a zero filling tensor is obtained;
s103: and adding the two zero-filling tensors to obtain an updated matrix product state.
6. A quantum secret sharing system based on tensor network state dynamic compression is characterized in that the quantum secret sharing method of any one of claims 1 to 5 is adopted in the system to carry out quantum secret sharing, and quantum signature, quantum authentication or quantum key distribution is realized.
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CN117240458B (en) * 2023-11-13 2024-04-02 信联科技(南京)有限公司 Multi-secret sharing method for user self-choice sub-secret

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