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

TL;DR

This paper introduces two general methods to determine the strong converse exponent in quantum hypothesis testing for various correlated quantum states, linking it to the Hoeffding anti-divergence and regularized Re9nyi divergences.

Contribution

It presents novel approaches for calculating the strong converse exponent applicable to a broad class of correlated quantum states, expanding the theoretical framework.

Findings

Strong converse exponent equals Hoeffding anti-divergence.

Approach one applies to states with a factorization property.

Approach two applies to states with differentiable Re9nyi divergence.

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 R\'enyi $\alpha$-divergence in the parameter $\alpha$; 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 R\'enyi divergences of the two states.