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Title: Quantum Hypothesis Testing for Gaussian States: Quantum Analogues of χ2, t-, and F-Tests
Authors: Kumagai, W.
Hayashi, M. 
Issue Date: 2013
Citation: Kumagai, W., Hayashi, M. (2013). Quantum Hypothesis Testing for Gaussian States: Quantum Analogues of χ2, t-, and F-Tests. Communications in Mathematical Physics 318 (2) : 535-574. ScholarBank@NUS Repository.
Abstract: 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 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 the χ2, t-, and F-tests as optimal tests in the respective settings. © 2013 Springer-Verlag Berlin Heidelberg.
Source Title: Communications in Mathematical Physics
ISSN: 00103616
DOI: 10.1007/s00220-013-1678-1
Appears in Collections:Staff Publications

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