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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