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arXiv:quant-ph/0703159 · Quantum Information and Computation

Single qubit quantum secret sharing with improved security

G.P. He, Z.D. Wang

Published Jan 1, 2010• 15 citations
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Abstract

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.

DOI
10.26421/qic10.1-2-3

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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.
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.
Recently, position-based quantum cryptography has been claimed to be unconditionally secure. On the contrary, here we show that the existing proposals for position-based quantum cryptography are, in fact, insecure if entanglement is shared among two adversaries. Specifically, we demonstrate how the adversaries can incorporate ideas of quantum teleportation and quantum secret sharing to compromise the security with certainty. The common flaw to all current protocols is that the Pauli operators always map a codeword to a codeword (up to an irrelevant overall phase). We propose a modified scheme lacking this property in which the same cheating strategy used to undermine the previous protocols can succeed with a rate of at most 8585%85. We prove the modified protocol is secure when the shared quantum resource between the adversaries is a two- or three-level system.
Abstract In the paper (EPJ Quant. Technol. 10:29, 2023), Kuo et al. proposed a multiparty quantum secret sharing protocol based on a novel structure and single qubits. Owing to the absence of an entanglement state, the proposed protocol is more practical than other quantum secret sharing protocols which use entanglement properties. Therefore, we study the security of the proposed protocol and find there exists a security loophole in the n-party ( n≥4n\geq 4n≥4 n ≥ 4 ) secret sharing case in it, that is, two dishonest agents can collude to obtain (part of) Alice’s secret without the help of the other agents. In order to overcome the security loophole, we give an improved protocol and make a security analysis for it. By calculating, the qubit efficiency of the three-party case in it is equal to 18\frac{1}{8}81​ 1 8 , which is higher than that in Hillery et al.’s protocol (Phys. Rev. A 59:1829, 1999).