Asymptotic state discrimination on lattice systems

Asymptotic hypothesis testing in its simplest form is about discriminating two states of a lattice system, based on measurements on finite blocks that asymptotically cover the whole lattice. In general, it is not possible to discriminate the local states with certainty, and one's aim is to minimize the probability of error, subject to certain constraints. Hypothesis testing results show that, in various settings, the error probabilities vanish with an exponential speed, and the decay rates coincide with certain relative-entropy like quantities. Apart from giving computable closed expressions for the error exponents, the importance of these results lies in providing an operational interpretation for the given relative entropy-like quantities. Here we present such identities in the settings of Stein's lemma and the Chernoff and the Hoeffdings bounds for various classes of correlated states on cubic lattices.