Abstract
In order to improve the efficiency of quantum secret sharing, quantum ramp secret sharing schemes were proposed (Ogawa et al., Phys. Rev. A 72, 032318 [2005]), which had a trade-off between security and coding efficiency. In quantum ramp secret sharing, partial information about the secret is allowed to leak to a set of participants, called an intermediate set, which cannot fully reconstruct the secret. This paper revisits the size of a share in the quantum ramp secret scheme based on a relation between the quantum operations and the coherent information. We also propose an optimal quantum ramp secret sharing scheme.
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References
Shamir, A.: Commun. ACM. 22, 612–613 (1979).
Hillery, M., Buzek, V., Berthiaume, A.: Phys. Rev. A. 59 (3), 1829–1834 (1999).
Stinson, A. D.: Cryptography Theory and Practice, 3rd edn. Chapman&Hall/CRC, 2006.
Ogawa, T., Sasaki, A., Iwamoto, M., Yamamoto, H.: Phys. Rev. A. 72, 032318 (2005).
Matsumoto, R: arXiv:http://arXiv.org/abs/quant-ph/1405.0149v5, 2014.
Zhang, P., Matsumoto, R.: Q. Inf. Process. 14 (2), 715–729 (2015).
Schumacher, B., Nielsen, M. A.: Quantum data processing and error correction. Phys. Rev. A. 54, 2629–2635 (1996).
Holevo, A. S., Shirokov, M. E.: Problems Inf. Trans. 46 (3), 201–218 (2010).
Westmoreland, M., Schumacher, B.: Lect. Notes Comput. Sci. 1509, 285–295 (1998).
Araki, H., Lieb, E.: Commun. Math. Phys. 18, 160–170 (1970).
Nielsen, M. A., Caves, C. M., Schumacher, B., Barnum, H.: Proc. R. Soc. London Series Mat. Phys. Eng. Sci. 454, 277–304 (1998).
Lloyd, S.: Phys. Rev. A. 55, 1613–1622 (1997).
Grishanin, B. A., Zadkov, V. N.: Phys. Rev. A. 62, 032303 (2000).
Horodecki, M., Oppenheim, J., Winter, A.: Nature. 436 (7051), 673–676 (2005).
Rietjens, K., Schoenmakers, B., Tuyls, P.: Int. Symp. Information Theory, pp. 1598–1602. Adelaide, Australia, 2005.
Ahlswede, R., Lober, P.: IEEE Trans. Inf. Theory. 47(1), 474–478 (2001).
Acknowledgments
his work was supported by Postdoctoral Science Foundation of China under grant No.2015M582686 and No.2015M580805.
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Xiao, H., Wang, H. & Wang, B. Quantum Ramp Secret Sharing Scheme and Quantum Operations. Int J Theor Phys 55, 3807–3815 (2016). https://doi.org/10.1007/s10773-016-3010-2
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DOI: https://doi.org/10.1007/s10773-016-3010-2