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arXiv · 1409.3897

Tight asymptotic bounds on local hypothesis testing between a pure bipartite state and the white noise state

Masahito Hayashi·Masaki Owari
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Abstract

We consider asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state $\ket{\Psi}$ and the completely mixed state under one-way LOCC (local operations and classical communications), two-way LOCC, and separable POVMs. As a result, we derive the Hoeffding bounds under two-way LOCC POVMs and separable POVMs. Further, we derive a Stein's lemma type of optimal error exponents under one-way LOCC, two-way LOCC, and separable POVMs up to the third order, which clarifies the difference between one-way and two-way LOCC POVM. Our study gives a very rare example in which the optimal performance under the infinite-round two-way LOCC is also equal to that under separable operations and can be attained with two-round communication, but not attained with the one-way LOCC.

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Masahito Hayashi, Masaki Owari. 2014-09-13. Tight asymptotic bounds on local hypothesis testing between a pure bipartite state and the white noise state. https://doi.org/10.1109/tit.2017.2687932

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