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arXiv:quant-ph/0605225

A quantum secret sharing scheme among three parties ultilizing four-qubit Smolin bound entangled state

Ya-Fei Yu, Yi Xu, Jin Liu

Published May 26, 2006• 2 citations
arXivHTMLPDF

Abstract

Four-qubit Smolin bound entangled state has a distinct feature: the state is not distillable when every qubit is seperated from each other; but it makes two separated qubit entangled if the other qubits group together. Here the feature is applied to quantum secret sharing, a QSS protocol similar to Ekert 91 protocol of QKD is proposed. The security problem, disadvantage and advantageof this protocol are disscused.

DOI
10.48550/arxiv.quant-ph/0605225

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Four-qubit Smolin bound entangled state has a distinct feature: the state is not distillable when every qubit is seperated from each other; but it makes two separated qubit entangled if the other qubits group together. Here the feature is applied to quantum secret sharing, a QSS protocol similar to Ekert 91 protocol of QKD is proposed. The security problem, disadvantage and advantageof this protocol are disscused.
It was indicated [Yu 2007 Phys. Rev. A 75 066301] that a previous proposed quantum secret sharing (QSS) protocol based on Smolin states [Augusiak 2006 Phys. Rev. A 73 012318] is insecure against an internal cheater. Here we build a different QSS protocol with Smolin states alone, and prove it to be secure against known cheating strategies. Thus we open a promising venue for building secure QSS using merely Smolin states, which is a typical kind of bound entangled states. We also propose a feasible scheme to implement the protocol experimentally.
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.
As an important resource of the quantum information engineering, to explore its' possible applications and limits in the field of the secure communication is very necessary. In the paper we analyse the problem of the security of quantum secret sharing with Smolin bound entangled states as the channel quantum state. An intercept-resend strategy of the inner of the legal communicators is proposed to attack the security without be detected by the checking procedure with comparing the results of single-qubit measurement. A conclusion that quantum secret sharing only with Smolin bound entangled states as the channel quantum state isnot unconditionally secure is attained, and a general proof in terms of the quantum correlation is given.