### Abstract

We apply the recent results of Hiai [J. Math. Phys. 49, 032112 (2008)] to the asymptotic hypothesis testing problem of locally faithful shift-invariant quasifree 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.

Original language | English |
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Article number | 072104 |

Journal | Journal of Mathematical Physics |

Volume | 49 |

Issue number | 7 |

DOIs | |

Publication status | Published - Aug 18 2008 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Mosonyi, M., Hiai, F., Ogawa, T., & Fannes, M. (2008). Asymptotic distinguishability measures for shift-invariant quasifree states of fermionic lattice systems.

*Journal of Mathematical Physics*,*49*(7), [072104]. https://doi.org/10.1063/1.2953473