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

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 $\alpha$-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 Rényi divergences of the two states.

v3:21 pages, essentialy the published version

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• Fermionic Quasi-free States and Maps in Information Theory
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• On the error exponents of binary state discrimination with composite hypotheses
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• Quantum Rényi divergences and the strong converse exponent of state discrimination in operator algebras
• Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence
• Quantum dichotomies and coherent thermodynamics beyond first-order asymptotics