Error exponents in hypothesis testing for correlated states on a spin chain

Understand

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.