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Chinese Physics

High-dimension multiparty quantum secret sharing scheme with Einstein–Podolsky–Rosen pairs

Chen Pan, Deng Fu-Guo, Long Gui-Lu

Published Sep 21, 2006• 49 citations
Publisher

Abstract

In this paper a high-dimension multiparty quantum secret sharing scheme is proposed by using Einstein–Podolsky–Rosen pairs and local unitary operators. This scheme has the advantage of not only having higher capacity, but also saving storage space. The security analysis is also given.
DOI
10.1088/1009-1963/15/10/007

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This paper presents a scheme for high-capacity three-party quantum secret sharing with quantum superdense coding, following some ideas in the work by Liu et al (2002 Phys. Rev. A 65 022304) and the quantum secret sharing scheme by Deng et al (2008 Phys. Lett. A 372 1957). Instead of using two sets of nonorthogonal states, the boss Alice needs only to prepare a sequence of Einstein–Podolsky–Rosen pairs in d -dimension. The two agents Bob and Charlie encode their information with dense coding unitary operations, and security is checked by inserting decoy photons. The scheme has a high capacity and intrinsic efficiency as each pair can carry 2lb d bits of information, and almost all the pairs can be used for carrying useful information.
Based on the Einstein-Podolsky-Rosen (EPR) entangled state and the unitary operation, a quantum secret-sharing (QSS) scheme on access structure is proposed. The participants randomly choose their private keys themselves. Each participant keeps one private key even though he belongs to several qualified subsets. In the recovery, the participants in the qualified subset perform the unitary operations on the EPR pairs, and recover the secret through the Bell-state measurement. Compared to the existing QSS schemes on (n, n) or (t, n) structure, the proposed scheme on access structure is more flexible in practice.
A multiparty quantum secret sharing scheme is proposed to utilize the magic properties of entanglement swapping. In this scheme, a set of (2N-1) EPR pairs is used to encode and distribute a secret message to (N-1) parties. Each secret message will be split into (N-1) packets. By performing the local unitary operations and entanglement swapping, each classical bit packet will be encoded secretly into Bell states so no subset of parties but their entire cooperation can read out the original secret message. The security of this proposed scheme is also considered.
A scheme for multiparty quantum state sharing of an arbitrary two-particle state is presented with Einstein-Podolsky-Rosen pairs. Any one of the NNN agents has the access to regenerate the original state with two local unitary operations if he collaborates with the other agents, say the controllers. Moreover, each of the controllers is required to take only a product measurement ${\ensuremath{\sigma}}_{x}\ensuremath{\bigotimes}{\ensuremath{\sigma}}_{x}$ on his two particles, which makes this scheme more convenient for the agents in the applications on a network than others. As all the quantum source can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. With a new notation for the multipartite entanglement, the sender need only publish two bits of classical information for each measurement, which reduces the information exchanged largely.