Large deviations and Chernoff bound for certain correlated states on a spin chain

Abstract

In this paper we extend the results of Lenci and Rey-Bellet on the large deviation upper bound of the distribution measures of local Hamiltonians with respect to a Gibbs state, in the setting of translation-invariant finite-range interactions. We show that a certain factorization property of the reference state is sufficient for a large deviation upper bound to hold and that this factorization property is satisfied by Gibbs states of the above kind as well as finitely correlated states. As an application of the methods the Chernoff bound for correlated states with factorization property is studied. In the specific case of the distributions of the ergodic averages of a one-site observable with respect to an ergodic finitely correlated state the spectral theory of positive maps is applied to prove the full large deviation principle.

some typos corrected, short proof of Lemma A.2 added

References in corpus (4)

• The Quantum Chernoff Bound
• Error exponents in hypothesis testing for correlated states on a spin chain
• Large deviations in quantum lattice systems: one-phase region
• Typical support and Sanov large deviations of correlated states

Cited by in corpus (5)

• The large deviation approach to statistical mechanics
• Generalized relative entropies and the capacity of classical-quantum channels
• Error exponents in hypothesis testing for correlated states on a spin chain
• Hypothesis testing for Gaussian states on bosonic lattices
• Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems