Abstract
Quantum secret sharing allows each player to have classical information for secret sharing in quantum mechanical ways. In this work, we construct a class of quantum states on which players can quantumly perform secret-sharing secure against dishonest players as well as eavesdropper. We here call them the genuine secret-sharing states. In addition, we show that if N players share an N-party genuine secret-sharing state, then arbitrary M players out of the total players can share an M-party genuine secret-sharing state by means of local operations and classical communication on the state, where \(N > M \ge 2\). We also define the distillable rate with respect to the genuine secret-sharing state and explain the connection between the distillable rate and the relative entropy of entanglement.
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Acknowledgements
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (Grant No. NRF-2019R1A2C1006337) and the Ministry of Science and ICT, Korea, under the Information Technology Research Center support program (Grant No. IITP-2020-2018-0-01402) supervised by the Institute for Information and Communications Technology Promotion. S.L. acknowledges support from Research Leave Program of Kyung Hee University in 2018.
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Choi, M., Lee, S. Genuine secret-sharing states. Quantum Inf Process 20, 47 (2021). https://doi.org/10.1007/s11128-021-02988-3
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DOI: https://doi.org/10.1007/s11128-021-02988-3