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|Title:||Quantum Hypothesis Testing for Gaussian States: Quantum Analogues of χ2, t-, and F-Tests||Authors:||Kumagai, W.
|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. https://doi.org/10.1007/s00220-013-1678-1||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||URI:||http://scholarbank.nus.edu.sg/handle/10635/126299||ISSN:||00103616||DOI:||10.1007/s00220-013-1678-1|
|Appears in Collections:||Staff Publications|
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