Quantum hypothesis testing for quantum Gaussian states: Quantum analogues of chi-square, t and F tests

Abstract

We treat quantum counterparts of testing problems whose optimal tests are given by chi-square, t and F tests. These quantum counterparts are formulated as quantum hypothesis testing problems concerning quantum Gaussian states families, and contain disturbance parameters, which have group symmetry. Quantum Hunt-Stein Theorem removes a part of these disturbance parameters, but other types of difficulty still remain. In order to remove them, combining quantum Hunt-Stein theorem and other reduction methods, we establish a general reduction theorem that reduces a complicated quantum hypothesis testing problem to a fundamental quantum hypothesis testing problem. Using these methods, we derive quantum counterparts of chi-square, t and F tests as optimal tests in the respective settings.

34 pages, 3 figures

References in corpus (8)

• The Quantum Chernoff Bound
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Phase estimation for thermal Gaussian states
• Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
• Hypothesis testing for Gaussian states on bosonic lattices
• Quantum hypothesis testing with group symmetry
• Quantum U-statistics

Cited by in corpus (2)

• Compression for quantum population coding
• Binary Discrimination in Quantum Systems via Hypothesis Testing