Optimization of Entanglement Distillation Protocols via Group Theoretical Tools

Bachelor thesis (2020)

Authors

S.E.D. Jansen Electrical Engineering, Mathematics and Computer Science

Contributors

D. Elkouss Coronas Quantum Information and Software - EEMCS (supervisor 1)
Dion Gijswijt Discrete Mathematics and Optimization - EEMCS (supervisor 1)
M. Blaauboer QN/Blaauboer Group - AS (supervisor 2)
J.G. Spandaw Analysis - EEMCS (supervisor 2)
Faculty
Applied Sciences
Copyright: © 2020 S.E.D. Jansen
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Published Date

10-07-2020

Language

English

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Faculty

Applied Sciences

Abstract

This thesis deals with n-to-1 entanglement distillation protocols for bipartite quantum systems in a group theoretical setting. The local operations in the protocols are restricted to Clifford operations. An efficient representation of the elements of the Clifford group in terms of binary matrices is presented. Moreover, a characterization of the subgroup of the Clifford group which leaves the fidelity and the success probability invariant is given. Based on this characterization, a novel approach for the optimization of distillation protocols is presented: instead of checking every element of the Clifford group individually, it is sufficient to consider one element of every right coset of this subgroup. These new insights are used to find optimal protocols for n = 2, 3, 4 and 5.