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Searching for optimal quantum secret sharing scheme based on local distinguishability

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Abstract

The (k, n)-threshold quantum secret sharing scheme is an important and difficult field in quantum information processing and quantum cryptography. In this paper, the (k, n)-threshold quantum secret sharing scheme based on local operations and classical communication (LOCC-QSS) is investigated. Firstly, in order to effectively study the LOCC-QSS scheme, digital and graphical representations of judgement space are introduced creatively. These representations are simple and convenient. Secondly, an algorithm is designed to search optional states for any given k and n. For optional states, the unambiguous probability equals 0 when x participants cooperate (x < k). Thirdly, a method is proposed to decrease the guessing probability. Some schemes which are more secure than existing ones can be obtained further. Last but not least, the conditions of optimal LOCC-QSS schemes are given for the first time. Our research will be helpful for the development of LOCC-QSS scheme.

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Acknowledgements

This work was supported by the National Key R&D Program of China (2017YFB0802703), NSFC (Grant Nos. 61671087, 61272514, 61170272, 61003287, U1836205), the Fok Ying Tong Education Foundation (Grant No. 131067), the Major Scientific and Technological Special Project of Guizhou Province (Grant No. 20183001), the Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant Nos. 2018BDKFJJ016, 2019BDKFJJ014), the Foundation of State Key Laboratory of Public Big Data (Grant No. 2018BDKFJJ018) and the Fundamental Research Funds for the Central Universities (Grant Nos. 2019XD-A02, 2020RC38) and sponsored by CCF-Tencent Open Fund WeBank Special Funding (CCF-WebankRAGR20180104).

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Authors and Affiliations

  1. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Zhao Dou, Gang Xu, Xiu-Bo Chen, Xin-Xin Niu & Yi-Xian Yang

  2. State Key Laboratory of Public Big Data, Guizhou University, Guiyang, 550025, Guizhou, China

    Gang Xu, Xiu-Bo Chen, Xin-Xin Niu & Yi-Xian Yang

  3. School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yu Yang

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  1. Zhao Dou
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  2. Gang Xu
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  3. Xiu-Bo Chen
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  4. Xin-Xin Niu
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  5. Yi-Xian Yang
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  6. Yu Yang
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Correspondence to Xiu-Bo Chen.

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Appendix: The pseudo-code of our searching algorithm

Appendix: The pseudo-code of our searching algorithm

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Dou, Z., Xu, G., Chen, XB. et al. Searching for optimal quantum secret sharing scheme based on local distinguishability. Quantum Inf Process 19, 368 (2020). https://doi.org/10.1007/s11128-020-02809-z

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