CN111865581A - Quantum secret sharing method and quantum communication system based on tensor network - Google Patents

Abstract

The invention discloses a quantum secret sharing method and a quantum communication system based on a tensor network. The quantum state is reconstructed by using the corresponding relationship between classical information and quantum information, and the distributor realizes the division of secrets by combining the AKLT model and the matrix product state representation. The sub-secret is then distributed to the participants through classical authentication channels and quantum channels. Finally, secret reconstruction is based on the theory of tensor network state and the (n,n) threshold group recovery protocol. The scalability of secret information, the scalability of matrix product representation of quantum many-body states, transfer characteristics and non-uniqueness are the biggest innovations of this scheme, which ensure the security and reliability of quantum communication, and solve the problem that the existing quantum state secret sharing cannot be achieved. The problem of dynamic construction. The diversity of matrix product state representation and the simple graphical representation corresponding to tensor networks make the scheme have good application prospects in the fields of quantum state sharing and information security in quantum networks.

Description

Quantum secret sharing method and quantum communication system based on tensor network

technical field

The present invention relates to quantum communication technology, more particularly, to a quantum secret sharing method and quantum communication system based on tensor network.

Background technique

In quantum communication systems, the security of the existing quantum state secret sharing schemes mostly depends on the transmission protocol, and the expansion of the initial secret state is not considered, so that these quantum state secret sharing schemes cannot achieve dynamic functions. If the participant joins and the old participant quits, the initial secret state must be discarded.

However, since the emergence of quantum computing, people have paid more and more attention to the theory and application of tensor network state, which is a state that can be represented by mathematical graphs and is an entangled state. Whether the algorithm of tensor network state can be applied to quantum state secret sharing, so that the non-uniqueness of the matrix product state corresponding to the same state can break through the limitation of the existing quantum state secret sharing scheme that cannot achieve dynamic functions. Therefore, the introduction of tensor network state is a breakthrough and trend in the design of quantum state secret sharing scheme. In addition, matrixing the quantum state is to use the matrix product to represent a multi-particle entangled state. The advantage is that the matrix product state can be related to a simple graphical representation.

In view of the above two innovations and advantages, it is necessary to design a quantum state secret sharing method combining matrix product state algorithm and graph state.

SUMMARY OF THE INVENTION

In view of this, the present invention first provides a quantum secret sharing method based on a tensor network, which utilizes the weight of the tensor network to realize the scalability of sharing quantum states, and solves the problem that the quantum secret state sharing scheme cannot achieve dynamic changes.

For achieving the above object, the concrete technical scheme adopted in the present invention is as follows:

A quantum secret sharing method based on tensor network, the key lies in including the following steps:

n表示参与者的数量；S1: The distributor prepares the quantum state secret information to be shared into sub-secret information according to the predetermined tensor network model according to the number of participants, and the sub-secret information includes the physical index information of each node in the tensor network model| σ _i > and bond index information

n represents the number of participants;

S2: The distributor sends the physical index information |σ _i > of each node to the corresponding participant P _i through the quantum channel, and announces h(·) and h( _xi ); where h(·) represents the predetermined a secure hash function, h( _xi ) represents the identity verification information calculated according to the identity information _xi of each participant according to a predetermined secure hash function;

S3: Each participant confirms whether they are eavesdropped by checking whether the received physical index information |σ _i > is entangled, and confirms that they have not been eavesdropped, then feed back the authentication information h' ( _xi ) to the distributor; if h( _xi )=h'( _xi ), the distributor considers the participant to be a legitimate participant, and sends the corresponding key indicator information to it through the classical channel

S4: Each participant sends the identity verification information h"(x _i ) calculated according to the predetermined secure hash function through the classical channel; if h(x _i )=h"(x _i ), the participant is a legal participant , each legal participant transmits the received physical index information |σ _i > and key index information to each other

后，按照步骤S1预定张量网络模型恢复分发者需要共享的量子态秘密信息。S5: Any participant collects physical index information |σ _i > and key index information corresponding to all legal participants

Then, according to the predetermined tensor network model in step S1, the quantum state secret information that the distributor needs to share is restored.

Optionally, the predetermined tensor network model in step S1 adopts a matrix product state tensor network model, a tree-like tensor network model, a projected entanglement pair state tensor network model or a multi-scale entanglement recombination hypothesis tensor network model.

Optionally, the number of participants is at least two.

Optionally, the distributor will need to share the quantum state secret information to prepare sub-secret information according to the AKLT model.

Optionally, when the predetermined tensor network model in step S1 adopts the matrix product state tensor network model and the number of participants is 3, the AKLT model is:

其中|ψ>表示含有需要共享的量子态秘密信息的量子多体系统。

where |ψ> denotes a quantum many-body system containing the secret information of the quantum state that needs to be shared.

Optionally, the identity information _xi of the respective participants adopts the respective device physical address information or identity number information.

The present invention also refers to a quantum communication system, the key of which is: adopting any of the quantum secret sharing methods described above to perform quantum secret sharing for realizing quantum signature, quantum authentication or quantum key distribution.

The technical effect of the present invention is:

Using this method, the system security and reliability are higher, the scalability of secret information is stronger, and the dynamic function of secret sharing is more convenient to realize, and it has a good application prospect in the field of quantum state sharing and information security in quantum networks. It can be further applied in quantum cryptography protocols such as quantum signature, authentication and key distribution, and can provide scientific theoretical methods for the design of secure, diverse and highly scalable quantum secure communication protocols.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and embodiments, in which:

Figure 1 shows the common four types of tensor network topology;

Fig. 2 is the topological structure diagram of using the AKLT model to prepare the matrix product state;

Fig. 3 is a working principle diagram of converting the matrix product state into a system of linear equations.

Detailed ways

In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, not for The invention is limited.

This embodiment first provides a quantum secret sharing method based on a tensor network. In order to better understand the inventive concept, the following briefly introduces the state theory of a tensor network and its diversity.

Tensor networks are not only used in mathematics, but also in physics, chemistry and machine learning. The basic idea is that an m×n matrix M with real entries can represent a linear mapping from R^n→R^m. Such a map can be depicted as a node with two edges. One edge represents the input space and the other edge represents the output space. In other words, a matrix is a two-dimensional array, and an n-dimensional array is called an n-order tensor or an n-tensor. For example, a number can be thought of as a zero-dimensional array, i.e. a point, so it is a 0-tensor that can be drawn as a node with zero edges. Likewise, a vector can be thought of as a one-dimensional array, and thus a 1-tensor. It is represented by a node with one edge. Matrices are two-dimensional arrays, and thus 2-tensors. It is represented by a node with two edges. A three-dimensional tensor is a three-dimensional array, and thus a node with three edges. The product of two or more tensors is represented by a set of nodes and edges, and the edges with the same index are collapsed, and then multiple tensors (including vectors, matrices, and higher-order tensors) are collapsed according to specific rules. , forming a network called a tensor network, and the nodes in each tensor network can be defined by physical indicators and key indicators.

As shown in Figure 1, the four most successful types of tensor networks are: the matrix product state (MPS) network model shown in Figure 1(a); the projection shown in Figure 1(b) The entangled pair state tensor network model (Projected Entangled Pair State, PEPS); the tree tensor network model (treetensor network, TTN) shown in Figure 1(c) and the multi-scale entanglement recombination hypothesis shown in Figure 1(d) A tensor network model (multiscaleentanglement renormalisation ansatz, MERA) where only tensors in the bottom layer have physical indices.

However, for a quantum many-body system with n degrees of freedom, it can be expressed as:

where the coefficients can be written as the product of multiple tensors:

Then there is:

Therefore, it is called a matrix product state (MPS), because the wave function of a quantum many-body system can be expanded under a certain set of orthonormal bases, and the number of orthonormal bases is infinite, so the matrix product state is not unique. .

Based on the above principles, this embodiment applies the matrix product state to the field of quantum state secret sharing, thereby proposing a quantum secret sharing method based on tensor networks. Taking three participants as an example, the matrix product state tensor network model is adopted. , which includes the following steps:

其中|ψ>表示含有需要共享的量子态秘密信息的量子多体系统，所述子秘密信息包括所述张量网络模型中每个节点的物理指标信息|σ₁>，|σ₂>，|σ₃>和键指标信息

S1: The distributor prepares the quantum state secret information to be shared into sub-secret information according to the AKLT model according to the matrix product state tensor network model according to the number of participants. The AKLT model is:

where |ψ> represents a quantum many-body system containing secret information of quantum states to be shared, and the sub-secret information includes physical index information of each node in the tensor network model |σ ₁ >, |σ ₂ >, | σ ₃ > and bond index information

S2: The distributor sends the physical index information of each node |σ ₁ >, |σ ₂ >, |σ ₃ > to the corresponding participants P ₁ , P ₂ , P ₃ through the quantum channel, and announces h(· ) and h(x ₁ ), h(x ₂ ), h(x ₃ ); where h(·) represents a predetermined secure hash function, and h(x _i ) represents a predetermined security hash function according to each participant’s identity information _xi The identity verification information calculated by the secure hash function of , in the specific implementation, the identity information of each participant can use their own device physical address information or identity number information;

S3: Each participant confirms whether they are eavesdropped by checking whether the received physical index information |σ ₁ >, |σ ₂ >, |σ ₃ > is entangled, and if it is confirmed that it has not been eavesdropped, then feed back through the classical channel according to the predetermined security. The authentication information h'(x _i ) calculated by the hash function is sent to the distributor; if h(x _i )=h'(x _i ), the distributor considers the participant to be a legitimate participant and sends it to it through the classical channel Corresponding key indicator information;

S4: Each participant sends the identity verification information h"(x _i ) calculated according to the predetermined secure hash function through the classical channel; if h(x _i )=h"(x _i ), the participant is a legal participant , each legal participant transmits the physical index information and key index information received by each other;

后，按照步骤S1预定的矩阵乘积态张量网络模型即可恢复分发者需要共享的量子态秘密信息。S5: Any participant collects physical indicator information |σ ₁ >, |σ ₂ >, |σ ₃ > and key indicator information corresponding to all legal participants

Then, according to the predetermined matrix product state tensor network model in step S1, the quantum state secret information that the distributor needs to share can be recovered.

This embodiment also provides a quantum communication system, which adopts the above quantum secret sharing method for quantum secret sharing, which is used to realize quantum signature, quantum authentication or quantum key distribution.

的值是由一个秘密矩阵M来决定的，使得矩阵乘积态张量网络模型中各张量的关联关系与每一个纠缠态的纠缠特性有关系，具体内容可参考文献：Affleck,Ian,TomKennedy,Elliott Lieb,and Hal Tasaki."Rigorous results on valence-bond groundstates in antiferromagnets."Physical Review Letters 59,no.7(1987):799-802.The AKLT model structure mentioned in the implementation process is shown in Figure 2, which belongs to the classical model in the field of quantum communication. The matrix in Figure 2

The value of is determined by a secret matrix M, so that the relationship between the tensors in the matrix product state tensor network model is related to the entanglement characteristics of each entangled state. For details, please refer to the literature: Affleck, Ian, TomKennedy, Elliott Lieb, and Hal Tasaki. "Rigorous results on valence-bond groundstates in antiferromagnets." Physical Review Letters 59, no. 7(1987): 799-802.

来求解秘密态|ψ>，其过程相当于图3所示的求解2个3元一次线性方程组，信息的不确定性仍为其本身,因此通过所获得信息得不到任何关于秘密的信息量。It can be seen from the technical solution provided in this embodiment that the initial secret is set in the quantum many-body system |ψ>. Assuming that a dishonest person or an attacker wants to steal secret information and intercepts two secrets, the

to solve the secret state |ψ>, the process is equivalent to solving two 3-element linear equations shown in Figure 3, the uncertainty of the information is still itself, so no information about the secret can not be obtained through the obtained information quantity.

The premise of the application of matrix product state tensor network is to construct a secret matrix M, and this premise makes the secret information scalable, the secret matrix is diversified, and becomes the innovation and advantage that other quantum secret sharing schemes do not have.

Due to the non-uniqueness of the matrix state, it is easy to realize the dynamic function of secret sharing. Once there is an update of the participants (that is, the old participant quits and the new participant joins), we can use a different secret matrix M to reconstruct the matrix product state so that the quantum state can continue to be used without affecting the shared state security.

使得参与者与量子多体态|Ψ>之间是相互独立的，即当参与者个人进行测量时，并不能够获取到自己手中的信息，因为子秘密信息会随着测量，通过矩阵乘积操作将秘密转移出去。值得注意的是，秘密信息的转移并不意味着任意的物理上的操作或者改变态的本身，其仅仅是对物理态的重新标记。In addition, the application of the matrix product state not only makes the scheme more convenient for graphical representation, but more importantly, the |σ ₁ >, |σ ₂ >, |σ ₃ > and |σ 3 > in |Ψ>

Make the participants and the quantum many-body state |Ψ> independent of each other, that is, when the participants personally measure, they cannot obtain the information in their own hands, because the sub-secret information will be measured along with the measurement, through the matrix product operation. Secretly transferred out. It is worth noting that the transfer of secret information does not imply any physical manipulation or changing the state itself, it is merely a relabeling of the physical state.

To sum up, it can be seen that a quantum secret sharing method and quantum communication system based on tensor network proposed by the present invention utilizes the correspondence between classical information and quantum information to reconstruct the quantum state, and the distributor combines the AKLT model and the matrix product state representation. The method realizes the division of secrets, and then distributes the sub-secrets to participants through classical authentication channels and quantum channels. Finally, secret reconstruction is based on the theory of tensor network state and the (n,n) threshold group recovery protocol. The scalability of secret information, the scalability of matrix product representation of quantum many-body states, transfer characteristics and non-uniqueness are the biggest innovations of this scheme, which ensure the security and reliability of quantum communication, and solve the problem that the existing quantum state secret sharing cannot be achieved. The problem of dynamic construction. The diversity of matrix product state representation and the simple graphical representation corresponding to tensor networks make the scheme have good application prospects in the fields of quantum state sharing and information security in quantum networks. More importantly, these theories can be further applied in quantum cryptographic protocols such as quantum signature, authentication and key distribution, and can provide scientific theoretical methods for the design of secure, diverse and highly scalable quantum secure communication protocols.

From the description of the above embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus a necessary general hardware platform, and of course hardware can also be used, but in many cases the former is better implementation. Based on this understanding, the technical solutions of the present invention can be embodied in the form of software products in essence or the parts that make contributions to the prior art, and the computer software products are stored in a storage medium (such as ROM/RAM, magnetic disk, CD-ROM), including several instructions to make a terminal (which may be a mobile phone, a computer, a server, or a network device, etc.) execute the methods described in the various embodiments of the present invention.

The embodiments of the present invention have been described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific embodiments, which are merely illustrative rather than restrictive. Under the inspiration of the present invention, without departing from the scope of protection of the present invention and the claims, many forms can be made, which all belong to the protection of the present invention.

Claims (7)

1. a quantum secret sharing method based on tensor network, is characterized in that comprising the following steps: S1: The distributor prepares the quantum state secret information to be shared into sub-secret information according to the predetermined tensor network model according to the number of participants, and the sub-secret information includes the physical index information of each node in the tensor network model| σ _i > and bond index information

n represents the number of participants; S2: The distributor sends the physical index information |σ _i > of each node to the corresponding participant P _i through the quantum channel, and announces h(·) and h( _xi ); where h(·) represents the predetermined secure hash function, h( _xi ) represents the identity verification information calculated according to the predetermined secure hash function according to the identity information _xi of each participant; S3: Each participant confirms whether they are eavesdropped by checking whether the received physical index information |σ _i > is entangled, and confirms that they have not been eavesdropped, then feed back the authentication information h' ( _xi ) to the distributor; if h( _xi )=h'( _xi ), the distributor considers the participant to be a legitimate participant, and sends the corresponding key indicator information to it through the classical channel

S4: Each participant sends the identity verification information h"(x _i ) calculated according to the predetermined secure hash function through the classical channel; if h(x _i )=h"(x _i ), the participant is a legal participant , each legal participant transmits the received physical index information |σ _i > and key index information to each other

S5: Any participant collects physical index information |σ _i > and key index information corresponding to all legal participants

After that, according to the predetermined tensor network model in step S1, the quantum state secret information that the distributor needs to share is restored. 2. The quantum secret sharing method based on tensor network according to claim 1, is characterized in that: the predetermined tensor network model in step S1 adopts matrix product state tensor network model, tree tensor network model, projection entanglement A tensor network model is assumed for a state tensor network model or multiscale entanglement reorganization. 3 . The quantum secret sharing method based on tensor network according to claim 1 , wherein the number of participants is at least two. 4 . 4. The quantum secret sharing method based on a tensor network according to claim 1, wherein the distributor prepares the sub-secret information according to the AKLT model according to the quantum state secret information to be shared. 5. the quantum secret sharing method based on tensor network according to claim 4, is characterized in that: When the predetermined tensor network model in step S1 adopts the matrix product state tensor network model and the number of participants is 3, the AKLT model is:

where |ψ> denotes a quantum many-body system containing the secret information of the quantum state that needs to be shared. 6 . The quantum secret sharing method based on a tensor network according to claim 1 , wherein the identity information x _i of the respective participants adopts respective equipment physical address information or identity number information. 7 . 7. A quantum communication system, characterized in that the quantum secret sharing method according to any one of claims 1-6 is used for quantum secret sharing, for realizing quantum signature, quantum authentication or quantum key distribution.

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