  In this paper, we treat an asymptotic hypothesis testing (or state
discrimination with asymmetric treatment of errors) between an arbitrary fixed
bipartite pure state and the completely mixed state by one-way LOCC, two-way
LOCC, and separable 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 approximates the bounds for separable POVMs in the
parameter region where analytical bounds for separable POVMs are derived.
