Hypothesis testing for Gaussian states on bosonic lattices

TL;DR

This paper provides a complete solution for hypothesis testing bounds and Stein's lemma for Gaussian states on bosonic lattices, advancing quantum state discrimination methods.

Contribution

It offers a comprehensive analysis of asymptotic state discrimination for gauge-invariant Gaussian states on bosonic lattices, including Chernoff, Hoeffding bounds, and Stein's lemma.

Findings

Derived explicit formulas for Chernoff and Hoeffding bounds.

Proved Stein's lemma for gauge-invariant Gaussian states.

Enhanced understanding of quantum hypothesis testing in lattice systems.

Abstract

The asymptotic state discrimination problem with simple hypotheses is considered for a cubic lattice of bosons. A complete solution is provided for the problems of the Chernoff and the Hoeffding bounds and Stein's lemma in the case when both hypotheses are gauge-invariant Gaussian states with translation-invariant quasi-free parts.