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. In this talk, I present a general method, based on the analysis of the asymptotic Renyi entropies, to obtain the exact error exponents for various classes of correlated states on cubic lattices. The examples include the temperature states of quasi-free fermionic and bosonic lattices, finitely correlated states, and the discrimination problem of i.i.d. states with group symmetric measurements. The discrimination problem of temperature states of a spin chain with translation-invariant and finite-range interaction is also treated with a different method.

Paper reference: arXiv:0706.2141, arXiv:0707.2020, arXiv:0802.0567, arXiv:0808.1450, arXiv:0904.0704