# 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} }

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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