Entaglement sharing protocol via quantum error correcting code
Date
2012
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Quantum secret sharing concerns secure and reliable distribution of classical or quantum information by a dealer to a set of "players" such that authorized subsets of players can access full information and unauthorized subsets are denied any information whatsoever. Exploiting quantum secret sharing concepts and techniques, I introduce a new protocol of "entanglement sharing" wherein half of maximally entangled bipartite states arc encrypted into multipartitc states in such a way that unauthorized players can only establish shared separable (not entangled) states with the dealer. Only authorized subsets of players obtain entangled states, which enable quantum information tasks such as quantum teleportation. Entanglement sharing can reduce the size of shares to individual players by half depending on the choice of encoding operation, as I show with the [[4, 2, 2]] stabilizer code. In fact, the [[4, 2, 2]] stabilizer code induces an optimal and threshold entanglement sharing scheme. Furthermore, I propose a new secrecy condition of quantum ramp secret sharing based on the bipartite setting of entanglement sharing. Ramp secret sharing relieves the bandwidth requirement of a protocol by reducing the size of shares at a cost of information leakage. Although quantum ramp secret sharing has been studied, to date it has been a challenge to classify leaked information. In this thesis, I define classical and quantum information with respect to the channels through which information is transmitted, and determine whether the information leakage is classical or quantum. Finally, I establish hybrid entanglement sharing by introducing classical shares in non-perfect entanglement sharing schemes. Hybrid entanglement sharing exploits a technique of locking entanglement with classical information, and can be devised from any quantum error correcting code.
Description
Bibliography: p. 74-79
Keywords
Citation
Choi, R. H. (2012). Entaglement sharing protocol via quantum error correcting code (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/4931