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

TL;DR

This paper extends quantum hypothesis testing error bounds to correlated states on spin chains, including Gibbs and finitely correlated states, broadening the applicability of quantum Chernoff and Hoeffding bounds.

Contribution

It generalizes recent quantum error exponent results from product states to correlated states on spin chains with specific factorization properties.

Findings

Extended quantum Chernoff bounds to correlated states

Derived Hoeffding bounds for spin chain states

Applicable to Gibbs and finitely correlated states

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 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.