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

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 Szegos 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.