Currently, quantum secret sharing (QSS) schemes based on entangled states have not yet fully utilized the potential of the probability amplitude of entangled states. However, the probability amplitude is a key characteristic of quantum information science and possesses significant application prospects in the fields of quantum computing and quantum communication. It is worth noting that entangled states can be effectively represented by matrix product states (MPSs). The representation of entangled states using MPS can precisely reveal the entanglement characteristics closely related to the probability amplitude. This study first focuses on the representation of the W state by using MPS, an approach that allows us to determine the key conditions for W state to achieve quantum advantage in QSS. Subsequently, this research demonstrates that by representing entangled states with MPS, a W state can be compressed into a single photon state and a simplified matrix form, presenting an innovative technical path. Moreover, one of the most attractive features of our proposed QSS scheme is its ability to compress multiple different quantum states (represented by photons) into a unified state represented by a single photon. This characteristic endows our scheme with scalability and flexibility, meaning that the group of participants can be easily expanded or reduced according to their specific needs. The addition of new participants is managed by Alice, who is responsible for the distribution of quantum state shares. On the other hand, when a participant leaves the group, their old quantum state share can be simply ignored in the process of recovering the secret's quantum state, thereby simplifying the management process. Through this strategy, we can not only make effective use of entangled resources but also meet the various requirements of the system, including but not limited to communication security, data transfer rates, and system scalability. This research provides new perspectives and possibilities for the field of quantum information science and may have a significant influence on the development of the field.
Currently, quantum secret sharing (QSS) schemes based on entangled states have not yet fully utilized the potential of the probability amplitude of entangled states. However, the probability amplitude is a key characteristic of quantum information science and possesses significant application prospects in the fields of quantum computing and quantum communication. It is worth noting that entangled states can be effectively represented by matrix product states (MPSs). The representation of entangled states using MPS can precisely reveal the entanglement characteristics closely related to the probability amplitude. This study first focuses on the representation of the W state by using MPS, an approach that allows us to determine the key conditions for W state to achieve quantum advantage in QSS. Subsequently, this research demonstrates that by representing entangled states with MPS, a W state can be compressed into a single photon state and a simplified matrix form, presenting an innovative technical path. Moreover, one of the most attractive features of our proposed QSS scheme is its ability to compress multiple different quantum states (represented by photons) into a unified state represented by a single photon. This characteristic endows our scheme with scalability and flexibility, meaning that the group of participants can be easily expanded or reduced according to their specific needs. The addition of new participants is managed by Alice, who is responsible for the distribution of quantum state shares. On the other hand, when a participant leaves the group, their old quantum state share can be simply ignored in the process of recovering the secret's quantum state, thereby simplifying the management process. Through this strategy, we can not only make effective use of entangled resources but also meet the various requirements of the system, including but not limited to communication security, data transfer rates, and system scalability. This research provides new perspectives and possibilities for the field of quantum information science and may have a significant influence on the development of the field.
Quantum secret sharing (QSS), as a quantum extension of classical secret sharing, uses the basic principles of quantum mechanics to share information safely among multiple parties, providing a new paradigm for information security. As a key foundation for secure multiparty quantum communication and distributed quantum computing, QSS has attracted considerable attention since its emergence. Currently, research in this field includes both classical and quantum scenarios, and continuous progress has been made in both theoretical and experimental aspects. This paper first reviews the current development of QSS for classical information. In this regard, significant and parallel progress has been made in both discrete-variable QSS and continuous-variable QSS. The QSS protocols for sharing classical information, from entangled states to single photons and then to coherent light, have been continuously optimized to better utilize available resources and achieve more efficient implementation under current technological conditions. Meanwhile, round-robin, measurement-device-independent, and other protocols have been steadily improving the security of QSS. Next, one will focus on QSS scheme for quantum secrets, which begins with the symmetry of access structures and introduces basic (k, n) threshold protocols, dynamic schemes that support adaptive agent groups, and symmetric quantum information splitting through entanglement. It further introduces hierarchical quantum secret sharing schemes for asymmetric splitting of quantum information. Considering practical laboratory conditions of quantum states as resources, an overall discussion is conducted on quantum secret sharing with graph states. Afterwards, the design of a continuous-variable scheme for quantum secret sharing is outlined, and entanglement state sharing and quantum teleportation between multiple senders and receivers are introduced. Finally, this review discusses and outlines the future development directions of QSS, thereby inspiring readers to further study and explore the relevant subjects.
Quantum secret sharing is an important way to achieve secure communications, which has critical applications in the field of information security for its physical properties. According to the perspective of the practical applications, improving the confidentiality and integrity of secret sharing schemes is a good method to increase the security and reliability of communications. In this paper, we propose a quantum secret sharing scheme based on generator matrix segmentation and the structural features of quantum graph states. The security of the secure secret sharing scheme is guaranteed by the pattern of transferring information by stabilizers, scalability of the information and new recovery strategy provided by the entanglement of the related graph states. It puts forward an effective solution to the problem of matrix cycle period, where some numbers without the primitive element cannot construct the generation matrix. First of all, the physical properties of quantum bits (qubits), such as uncertainty principle, no-cloning theorem and indistinguishability, not only optimize the classical schemes but also ensure the absolute safety of communication. Secondly, the application of matrix segmentation makes secret information has better scalability. It improves the coding diversity and the difficulty in deciphering. Thirdly, the favorable entanglement properties and mature experiment preparation techniques of graph states provide an approach to the practical applications. The superiority of the yielded graph states is described in graphical fashion with an elegant stabilizer. Fourthly, the shuffling operation can ensure the independence of the message among participants. Therefore, Eve can not obtain any useful information by measuring randomly. Two group-recovery protocols are proposed to show the secret recovering processing through rebuilding sub-secrets among legal cooperative participants. In the scheme design, the dealer extracts the classical secret information according to the corresponding principle between the classical and quantum information, and divides the classical secret through generated matrix which is produced with the primitive elements in finite domain satisfying the linear independence for any k column vectors. Then the dealer encodes information into graph states and distributes particles to the legal participants with unitary operations. Subsequently, the credible center obtains sub-secrets by the theory of graph states and the group recovery protocol. He can achieve the initial classical secret via the inverse algorithm of matrix segmentation. After getting the classical secret, he recovers quantum secret according to the relationship between classical information and quantum information. Theoretical analysis shows that this scheme can provide better security and scalability of the information. It is appropriate to realize the secret sharing in the quantum network communication to protect secrets from eavesdropping. Also, it can provide an approach to designing diverse and scalable quantum secure communication schemes based on quantum graph states, the algorithm of matrix segmentation, and group-recovery protocol.
Quantum secret sharing (QSS) is a cryptographic protocol that utilizes fundamental principles of quantum mechanics to securely distribute and reconstruct secret information among multiple participants. Most existing protocols rely on entangled states (such as Bell and GHZ states), but in practical applications. The preparation of entangled state is constrained by a short quantum coherence time, low state fidelity, etc., which makes it difficult to implement entangled resource-dependent QSS protocols. In this work, a novel practical and verifiable multi-party QSS protocol is proposed based on orthogonal product states, which are easier to prepare than entangled states. During the protocol preparation stage, the secret distributor first converts pre-shared classical secret information into the corresponding orthogonal product states according to the encoding rules, and pre-shares a communication key with participants via quantum key distribution (QKD), which is used to hide the initial quantum sequence information through subsequent particle transformation operations. After preparing the orthogonal product states, the distributor reorganizes the particles by position, extracting particles at the same position from each state to form new sequences, shuffling their order, then applying Hadamard operations using a pre-shared key, inserting decoy particles, and sending the sequences to the participants. After receiving it, participants conduct eavesdropping detection, use the same key for the inverse transformations, retain one particle from each sequence, and sequentially pass the remaining particles until the last participant receives a complete set, triggering state verification with the arbiter distributor. If the verification is successful, the particles will be returned to the first participant and the return stage will follow the same procedure. Only after both the transmission and return stage verifications have passed, will the distributor reveal the initial particle positions, allowing participants to collaboratively reconstruct the secret. In the protocol, the secret distributor acts as an arbitrator to verify the particle state information together with participants at designated points (the end of the transmission stage and the end of the return stage) in order to determine whether the particle-state information is error-free during transmission. If the verification fails at either stage, the protocol will be terminated immediately. Meanwhile, considering that the number of participants may change during the execution of the protocol, a dynamic scheme for personnel changes is designed to ensure the flexibility of the protocol. Through the analysis of possible internal and external attacks, It can be proven that our protocol can effectively resist the existing common attack. Using Qiskit simulation experiments, the core quantum procedures of the protocol can be successfully modeled. The experimental results provide strong computational validation of the theoretical feasibility of the protocol.
Quantum secret sharing (QSS) is a cryptographic multiparty communication technique in which a secret is divided and shared among N parties and then securely reconstructed by (N-1) cooperating parties, making it perfect for storing and sharing highly sensitive data. Challenges in high dimensional state preparation, transformation and detection, the key steps of any QSS protocol, have so far hindered experimental realisation. Here, by taking advantage of the high-dimensional encoding space accessible by a photon's orbital angular momentum, we present a toolbox for realising practical high-dimensional single photon QSS schemes that are easily scalable in both dimension and number of participants. Our implementations realised a new record in both the number of participants (N=10) and the dimensionality (d=11), with the latter facilitating the transfer of 2.89 bits of information per photon. This work is an important step towards securely distributing information across a network of nodes.
Quantum secret sharing （QSS） is one of the important branches of quantum cryptography， which is used to share a secret among multiple participants， and has great potential for applications in fields such as quantum computing and quantum communication. With the rapid development of quantum information， people have higher requirements for the number of users and security of quantum secret sharing. This article analyzes the entanglement characteristics of three entangled states， namely the continuous variable four component Bound Entanglement （BE） state， GHZ （Greenberger-Horn-Zeilinger） state， and Cluster state， and uses them as quantum resources to construct a four component quantum secret sharing scheme. The dependence of quantum secret sharing security on different physical parameters is theoretically calculated for each scheme. The results show that the secret key rate of different entangled state optical fields has a consistent relationship with the signal strength when four users cooperate. While the secret key rate in the BE entangled-state light field corresponding to the QSS scheme is balanced in orthogonal amplitude and orthogonal bit-phase components with a symmetric relationship when three users cooperate， the GHZ entangled-state and the Cluseter entangled-state light field corresponding to the QSS scheme show a larger secret key rate in a single orthogonal component.
With the rise of quantum computing, traditional cryptography is facing serious threats. Secret sharing, as an important primitive of cryptography, is also affected. Because secret sharing is widely used in many fields, researchers have started to explore quantum secret sharing (QSS). QSS uses basic principles of quantum mechanics to provide strong security and can protect against both eavesdropping and malicious attacks. However, most existing QSS studies focus on specific situations and lack the flexibility needed for complex multiparty environments. In this work, we propose a general QSS framework that can be applied to different scenarios. We first design a basic [Formula: see text] QSS protocol, and then extend it to support multiparty communication and dynamic changes in participants. Our security analysis shows that the proposed method keeps strong security, uses fewer resources, and works independently without the need for a trusted third party (TP). This protocol offers a unified solution that can meet different application needs and provides a new approach to handling diverse QSS tasks more efficiently.