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Quantum secret sharing for a general quantum access structure

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Abstract

Quantum secret sharing is a procedure for sharing a secret among a number of participants such that only certain subsets of participants can collaboratively reconstruct it, which are called authorized sets. The quantum access structure of a secret sharing is a family of all authorized sets. Firstly, in this paper, we propose the concept of decomposition of quantum access structure to design a quantum secret sharing scheme. Secondly, based on a maximal quantum access structure (MQAS) [D. Gottesman, Phys. Rev. A 61, 042311 (2000)], we propose an algorithm to improve a MQAS and obtain an improved maximal quantum access structure (IMQAS). Then, we present a sufficient and necessary condition about IMQAS, which shows the relationship between the minimal authorized sets and the players. In accordance with properties, we construct an efficient quantum secret sharing scheme with a decomposition and IMQAS. A major advantage of these techniques is that it allows us to construct a method to realize a general quantum access structure. Finally, we present two kinds of quantum secret sharing schemes via the thought of concatenation or a decomposition of quantum access structure. As a consequence, we find that the application of these techniques allows us to save more quantum shares and reduces more cost than the existing scheme.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, P.R. China

    Chen-Ming Bai, Zhi-Hui Li & Meng-Meng Si

  2. College of Computer Science, Shaanxi Normal University, Xi’an, 710119, P.R. China

    Yong-Ming Li

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  1. Chen-Ming Bai
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  2. Zhi-Hui Li
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  3. Meng-Meng Si
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Correspondence to Zhi-Hui Li.

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Bai, CM., Li, ZH., Si, MM. et al. Quantum secret sharing for a general quantum access structure. Eur. Phys. J. D 71, 255 (2017). https://doi.org/10.1140/epjd/e2017-80286-3

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  • DOI: https://doi.org/10.1140/epjd/e2017-80286-3

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