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arXiv · 1407.3567

Two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states

Milán Mosonyi·Tomohiro Ogawa
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Abstract

We present two general approaches to obtain the strong converse rate of quantum hypothesis testing for correlated quantum states. One approach requires that the states satisfy a certain factorization property; typical examples of such states are the temperature states of translation-invariant finite-range interactions on a spin chain. The other approach requires the differentiability of a regularized Rényi $α$-divergence in the parameter $α$; typical examples of such states include temperature states of non-interacting fermionic lattice systems, and classical irreducible Markov chains. In all cases, we get that the strong converse exponent is equal to the Hoeffding anti-divergence, which in turn is obtained from the regularized Rényi divergences of the two states.

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Milán Mosonyi, Tomohiro Ogawa. 2016-07-08. Two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states. https://doi.org/10.1109/tit.2015.2489259

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