Asymptotic local hypothesis testing between a pure bipartite state and the completely mixed state
Masaki Owari, Masahito Hayashi · Physical Review A · 2014
In this paper, we treat an asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state $|\ensuremath{\Psi}\ensuremath{\rangle}$ and the completely mixed state by one-way local operation and classical communication (LOCC), two-way LOCC, and separable positive operator-valued measures (POVMs). As a result, we derive single-letterized formulas for the Stein's lemma type of optimal error exponents under 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 in the whole region of 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 also almost approximate the bounds for separable POVMs in the parameter region where analytical bounds for separable POVMs are derived.