# Quantum Hypothesis Testing for Gaussian States: Quantum Analogues of χ2, t-, and F-Tests

@article{Kumagai2011QuantumHT,
title={Quantum Hypothesis Testing for Gaussian States: Quantum Analogues of $\chi$2, t-, and F-Tests},
author={Wataru Kumagai and Masahito Hayashi},
journal={Communications in Mathematical Physics},
year={2011},
volume={318},
pages={535-574}
}
• Published 28 October 2011
• Mathematics
• Communications in Mathematical Physics
We consider quantum counterparts of testing problems for which the optimal tests are the χ2, t-, and F-tests. These quantum counterparts are formulated as quantum hypothesis testing problems concerning Gaussian state families, and they contain nuisance parameters, which have group symmetry. The quantum Hunt-Stein theorem removes some of these nuisance parameters, but other difficulties remain. In order to remove them, we combine the quantum Hunt-Stein theorem and other reduction methods to…
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