  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 counter-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.
