Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems

TL;DR

This paper investigates the asymptotic distinguishability of shift-invariant quasi-free states in fermionic lattice systems, establishing bounds and entropy measures relevant for quantum hypothesis testing.

Contribution

It extends Szego's theorem to multivariate cases and applies recent theoretical results to derive error bounds and entropy measures for quantum states.

Findings

Existence of mean Chernoff and Hoeffding bounds

Derivation of mean relative entropy for the states

Optimal error exponents in quantum hypothesis testing

Abstract

We apply the recent results of F. Hiai, M. Mosonyi and T. Ogawa [arXiv:0707.2020, to appear in J. Math. Phys.] to the asymptotic hypothesis testing problem of locally faithful shift-invariant quasi-free states on a CAR algebra. We use a multivariate extension of Szego's theorem to show the existence of the mean Chernoff and Hoeffding bounds and the mean relative entropy, and show that these quantities arise as the optimal error exponents in suitable settings.