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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum secret sharing based on Smolin bound entangled states is not unconditionally secure

Ya‐Fei Yu, Zhiming Zhang

Published Oct 26, 2007• 0 citations

Abstract

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.

DOI: 10.1117/12.756387

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We considered a scenario recently suggested by Augusiak and Horodecki [Phys. Rev. A 73, 012318 (2006)], which used Smolin bound entangled states to share secrets. It is shown that a dishonest party can fully access secret information by an intercept-resend strategy without being detected.

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•Nov 28, 2007•0 citations

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.

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.

Four-qubit bound entangled Smolin states are generalized with help of the Hilbert-Schmidt formalism to any even number of qubits. They are shown to maximally violate simple correlation Bell inequalities and, as such, to reduce communication complexity, although they do not admit quantum security. They are also shown to serve for remote quantum information concentration, as in the case of the original four-qubit states. It is proven that the latter effect allows us to unlock some entanglement measures and classical correlations. Also the possibility of quantum secret sharing by the considered state is pointed out.