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

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.

Results extended to higher dimensional lattices, title changed. Submitted version

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• The Quantum Chernoff Bound
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Cited by in corpus (4)

• Generalized relative entropies and the capacity of classical-quantum channels
• Quantum state discrimination bounds for finite sample size
• Hypothesis testing for Gaussian states on bosonic lattices
• Super-exponential distinguishability of correlated quantum states