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Quantum secret sharing and quantum operations

Heling Xiao, Wang-Mei Guo, Xiao Wang

Published Jan 1, 2012• 0 citations
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Abstract

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.

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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.
Recently, an information theoretical model for quantum secret sharing (QSS) schemes was introduced. By using this model, we prove that pure state quantum threshold schemes (QTS) can be constructed from quantum MDS codes and vice versa. In particular, we consider stabilizer codes and give a constructive proof of their relation with QTS. Furthermore, we reformulate the monotone span program (MSP) construction according to the information theoretical model and check the recoverability and secrecy requirement. Finally, we consider QSS schemes which are based on quantum teleportation
In this paper we introduce a quantum information theoretical model for quantum secret sharing schemes. We show that quantum information theory provides a unifying framework for the study of these schemes. We prove that the information theoretical requirements for a class of quantum secret sharing schemes reduce to only one requirement (the recoverability condition) as a consequence of the no-cloning principle. We give also a shorter proof of the fact that the size of the shares in a quantum secret sharing scheme must be at least as large as the secret itself.
Recently, an information theoretical model for Quantum Secret Sharing (QSS) schemes was introduced. By using this model, we prove that pure state Quantum Threshold Schemes (QTS) can be constructed from quantum MDS codes and vice versa. In particular, we consider stabilizer codes and give a constructive proof of their relation with QTS. Furthermore, we reformulate the Monotone Span Program (MSP) construction according to the information theoretical model and check the recoverability and secrecy requirement. Finally, we consider QSS schemes which are based on quantum teleportation.
This paper studies the capacity limits for quantum secret sharing (QSS). The goal of a QSS scheme is to distribute a quantum secret among multiple participants, such that only authorized parties can recover it through collaboration, while no information can be obtained without such collaboration. We introduce an information-theoretic model for the rate analysis of QSS and its relation to compound quantum channels, following a similar approach as of Zou et al. (2015) on classical secret sharing. We establish a regularized characterization for the QSS capacity, and determine the capacity for QSS with dephasing noise.