Abstract
We study various error exponents in a binary hypothesis testing problem and extend recent results on the quantum Chernoff and Hoeffding bounds for product states to a setting when both the null hypothesis and the alternative hypothesis can be correlated states on a spin chain. Our results apply to states satisfying a certain factorization property; typical examples are the global Gibbs states of translation-invariant finite-range interactions as well as certain finitely correlated states.
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