Quantum secret sharing schemes and reversibility of quantum operations (7 pages)

S. K. Singh, R. Srikanth

Z.-j. Zhang

Chengcheng LI, Li‐Yi Hsu

Heling Xiao, Wang-Mei Guo, Xiao Wang

In this paper, we investigate the notion of quantum secret sharing (QSS) schemes based on quantum operations. We present the information theoretical model for QSS schemes using reversible operations and erase operations at first. We show that in pure state schemes, the recoverability requirement and the secrecy requirement are equivalent, which is regarded as a variant of nocloning theorem. By establishing a relation between the quantum information quantity--coherent information and QSS schemes, the upper bound of quantum information rate is given. Finally, we propose a pure state threshold scheme with the form of quantum operations. The operations formalism of quantum secret sharing generalizes the theorey of QSS, and provides a unifying framework for the study of these schemes.

Takeshi Okada, Hidenori Kuwakado, Masakatu Morii

Tomohiro Ogawa, Akira Sasaki, Mitsugu Iwamoto +1 more

Quantum secret sharing schemes encrypting a quantum state into a multipartite entangled state are treated. The lower bound on the dimension of each share given by Gottesman [Phys. Rev. A 61, 042311 (2000)] is revisited based on a relation between the reversibility of quantum operations and the Holevo information. We also propose a threshold ramp quantum secret sharing scheme and evaluate its coding efficiency.