Asymptotic local hypothesis testing between a pure bipartite state and the completely mixed state

Details Asymptotic local hypothesis testing between a pure bipartite state and the completely mixed state Asymptotic local hypothesis testing between a pure bipartite state and the completely mixed state

2011-05-19

arxiv.org/abs/1105.3789v1

Physics

Quantum Physics

14pages, 4 figures

Scientific paper

In this paper, we treat an asymptotic hypothesis testing between an arbitrary known bipartite pure state and the completely mixed state under one-way LOCC, two-way LOCC, and separable POVMs. As a result, we derive analytical formulas for the Stein's lemma type of optimal error exponents under all one-way LOCC, two-way LOCC and separable POVMs, the Chernoff bounds under one-way LOCC POVMs and separable POVMs, and the Hoeffding bounds under one-way LOCC POVMs without any restriction on a parameter and under separable POVMs on a restricted region of a parameter. We also numerically calculate the Chernoff and the Hoeffding bounds under a class of three step LOCC protocols in low dimensional systems, and show that these bounds not only outperform the bounds for one-way LOCC POVMs, but almost approximate the bounds for separable POVMs in the region of parameter where analytical bounds for separable POVMs are derived.

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