Two Approaches to Obtain the Strong Converse Exponent of Quantum Hypothesis Testing for General Sequences of Quantum States

© 2015 IEEE. We present two general approaches to obtain the strong converse exponent of simple 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.