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Can Smolin states alone lead to secure quantum secret sharing

Guang Ping He, Z. D. Wang, Yan-Kui Bai

Published Nov 28, 2007• 0 citations
OpenAlex

Abstract

It was indicated [Phys. Rev. A 75, 066301 (2007)] that a previous proposed quantum secret sharing (QSS) protocol based on Smolin states [Phys. Rev. A 73, 012318 (2006)] is insecure against an internal cheater. Here we build a new QSS protocol with Smolin states alone, and proved it to be secure against any cheating strategy. Thus we conclude that Smolin states alone can lead to secure QSS. We also propose a feasible scheme to implement the protocol experimentally.

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It was indicated [Phys. Rev. A 75, 066301 (2007)] that a previous proposed quantum secret sharing (QSS) protocol based on Smolin states [Phys. Rev. A 73, 012318 (2006)] is insecure against an internal cheater. Here we build a new QSS protocol with Smolin states alone, and proved it to be secure against any cheating strategy. Thus we conclude that Smolin states alone can lead to secure QSS. We also propose a feasible scheme to implement the protocol experimentally.
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.
Analyzing carefully an experimentally feasible non-entangled single qubit quantum secret sharing protocol and its modified version [Phys. Rev. Lett. 95, 230505 (2005); \textit{ibid}. 98, 028902 (2007)], it is found that both versions are insecure against coherent attacks though the original idea is so remarkable. To overcome this fatal flaw, here we propose a protocol with a distinct security checking strategy, which still involves single qubit operations only, making it possible to achieve better security of quantum secret sharing with current technology.
In a recent paper (Hwang et al 2011 Phys. Scr. 83 045004), a subtle quantum secret sharing (QSS) protocol was proposed. One major advantage of this protocol is its high efficiency; that is, it is more efficient than other QSS protocols using the Greenberger–Horne–Zeilinger states. However, we analyzed the security of this protocol and found that it is insecure for one agent who may deduce half of the information about the deal's secret directly just by his/her piece of secret. Finally, a feasible improvement of this QSS protocol is put forward.