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Physical Review A

Quantum secret sharing using product states

Li-Yi Hsu, Che‐Ming Li

Published Feb 28, 2005• 110 citations
Publisher

Abstract

This study proposes quantum secret sharing protocols using product states. The first two protocols adopt the quantum key distribution protocol using product states [Guo et al.Phys. Rev. A 64, 042301 (2001)]. In these two protocols, the sender does not reveal any information about the qutrits until confirming that each receiver has received a qutrit. This study also considers the security and some possible eavesdropping strategies. In the third proposed protocol, three-level Bell states are exploited for qutrit preparation via nonlocality swapping.

DOI
10.1103/physreva.71.022321

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This study proposes quantum secret sharing protocols using product states. The first two protocols adopt the quantum key distribution protocol using product states [Guo et al.Phys. Rev. A 64, 042301 (2001)]. In these two protocols, the sender does not reveal any information about the qutrits until confirming that each receiver has received a qutrit. This study also considers the security and some possible eavesdropping strategies. In the third proposed protocol, three-level Bell states are exploited for qutrit preparation via nonlocality swapping.
We propose an efficient quantum secret sharing scheme with orthogonal product states in the 3×3 Hilbert space. Different from Hsu and Li's scheme [Phys. Rev. A 71, 022321 (2005)], this scheme utilizes a novel distribution strategy which sends the qutrits of basis states and superpositions to two separated observers respectively. The theoretical analysis shows that the intrinsic efficiency for qutrits in this scheme approaches 100% and the total efficiency of this scheme is higher than that of the aforementioned scheme. Furthermore, the security and some possible eavesdropping strategies are also examined in this paper.
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.
Two schemes for quantum secret sharing of single-qubit state were proposed.A symmetric threequbit entangled state and an asymmetric three-qubit entangled state were used as quantum channel,respectively. The sender performs Bell-basis measurements on her particles,and the cooperator operates single-particle measurements on his particles,then the state receiver can reconstruct the original state by applying the appropriate unitary operation.The schemes can also be generalized to the case of arbitrary two-qubit and multi-particle entangled state.The security against certain eavesdropping attacks is also considered.These protocols are considered to be secure.
Boyer, Kenigsberg, and Mor [Phys.Rev.Lett.99, 140501(2007)] proposed a novel idea of semi-quantum key distribution where a key can be securely distributed between Alice who can perform any quantum operation and Bob who is classical. Extending the idea of “semiquantum” to other tasks of quantum information processing is of interest and worth considering. In this article, we consider the issue of semi-quantum secret sharing where a quantum participant Alice can share a secret key with two classical participants Bobs. After analyzing the existing protocol, we propose a new protocol of semi-quantum secret sharing. Our protocol is more realistic, since it utilizes product states instead of entangled states. We prove that any attempt of an adversary to obtain information necessarily induces some errors that the legitimate users could notice. 1
We develop a three-party quantum secret sharing protocol based on arbitrary dimensional quantum states. In contrast to the previous quantum secret sharing protocols, the sender can always control the state, just using local operations, for adjusting the correlation of measurement directions of three parties and thus there is no waste of resource due to the discord between the directions. Moreover, our protocol contains the hidden value which enables the sender to leak no information of secret key to the dishonest receiver until the last steps of the procedure.