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.
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.
Quantum secret sharing (QSS) has emerged as a promising avenue for storing secret with quantum-enhanced security. However, practical applications are hindered by the challenge for simultaneously implementing high-efficiency, high-security, and high-flexibility QSS with multiple users. Here we present an efficient, secure, and flexible QSS involving eight users with a continuous-variable eight-partite bound entanglement (BE) state, where only two nondegenerated optical parameter amplifiers are required. Such abilities are attributed to the generation of the eight-partite BE state with precise phase controlling systems and a large entanglement network, and fiber distribution with polarization-division multiplexing. In the QSS, a higher key rate can be demonstrated, when a secret is extracted through flexible combinations of more collaborative users. Our system may pave the way for the spatially separated multiuser quantum communications, while minimizing quantum hardware. Published by the American Physical Society 2024
Secret sharing is a conventional technique for realizing secure communications in information networks, where a dealer distributes to n players a secret, which can only be decoded through the cooperation of k (n/2<k≤n) players. In recent years, quantum resources have been employed to enhance security of secret sharing, which has been named quantum secret sharing (QSS). A multipartite bound entanglement (BE) state of an optical field, due to its special entanglement features, can be used in quantum networks to improve security and flexibility of communication. We design and experimentally demonstrate a QSS protocol, where the dealer modulates a secret on a four-partite BE state and then distributes the submodes of the BE state to four spatially separated players. The presented QSS scheme has the capability to protect secrets from eavesdropping and dishonest players, because a nonlocal and deterministic BE state is shared among four authorized players.
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 (QSS) is a typical multipartite cryptographic primitive, which is an important part of quantum communication network. Existing QSS protocols generally require basis matching, which would waste the precious quantum resource and increase the classical communication round. Moreover, the basis selection makes QSS face weak random security vulnerabilities. We propose an efficient QSS protocol without the basis matching. In the protocol, the dealer and partners share a polarization-momentum hyperentangled Greenberger-Horne-Zeilinger (GHZ) state and encode keys in the polarization degree of freedom (DOF). The dealer decodes the transmitted keys relying on the nonlocal hyperentanglement-assisted polarization GHZ state analysis. Our QSS protocol is unconditionally secure in theory. We develop simulation method to estimate its performance in practical environment. Our protocol has three advantages. First, it does not require the basis matching and can completely distinguish eight encoded polarization GHZ states, which increases the utilization rate of entanglement resources to 100 % and increases the key generation rate by an order of magnitude. Second, it only requires one round of classical communication, and thus reduces the key generation time by 69.4 % . Third, it can eliminate the weak random security vulnerabilities associated with the basis selection and enhance QSS’s practical security. Meanwhile, our protocol only uses linear optical elements, which makes it practically feasible. Our QSS protocol has application potential in the future quantum communication network.
With the rapid progress of quantum cryptography, secret sharing has been developed in the quantum setting for achieving a high level of security, which is known as quantum secret sharing (QSS). The first QSS scheme was proposed by Hillery et al. in 1999 [Phys. Rev. A, Vol. 59, p.1829 (1999)] based on entangled Greenberger-Horne-Zeilinger (GHZ) states. However, only 50% of the entangled quantum states are effective for eavesdropping detection and secret splitting in the original scheme. In this paper, we introduce a possible method, called measurement-delay strategy, to improve the qubit efficiency of the GHZ-based QSS scheme. By using this method, the qubit efficiency of the improved QSS scheme can reach 100% for both security detection and secret distribution. The improved QSS scheme can be implemented experimentally based on current technologies.
With the rapid progress of quantum cryptography, secret sharing has been developed in the quantum setting for achieving a high level of security, which is known as quantum secret sharing (QSS). The first QSS scheme was proposed by Hillery et al. in 1999 [Phys. Rev. A, Vol. 59, p.1829 (1999)] based on entangled Greenberger-Horne-Zeilinger (GHZ) states. However, only 50% of the entangled quantum states are effective for eavesdropping detection and secret splitting in the original scheme. In this paper, we introduce a possible method, called measurement-delay strategy, to improve the qubit efficiency of the GHZ-based QSS scheme. By using this method, the qubit efficiency of the improved QSS scheme can reach 100% for both security detection and secret distribution. The improved QSS scheme can be implemented experimentally based on current technologies.