Concurrence and Entanglement Entropy of Stochastic 1-Qubit Maps

Details Concurrence and Entanglement Entropy of Stochastic 1-Qubit Maps Concurrence and Entanglement Entropy of Stochastic 1-Qubit Maps

2009-03-07

arxiv.org/abs/0903.1340v1

Physical Review A 79 (2009) 052319

Physics

Quantum Physics

24 pages, 9 figures

Scientific paper

Explicit expressions for the concurrence of all positive and trace-preserving ("stochastic") 1-qubit maps are presented. We construct the relevant convex roof patterns by a new method. We conclude that two component optimal decompositions always exist. Our results can be transferred to 2xN-quantumsystems providing the concurrence for all rank two density operators as well as lower and upper bounds for their entanglement of formation. We apply these results to a study of the entanglement entropy of 1-qubit stochastic maps which preserve axial symmetry. Using analytic and numeric results we analyze the bifurcation patterns appearing in the convex roof of optimal decompositions and give results for the one-shot (Holevo-Schumacher-Westmoreland) capacity of those maps.

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