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Reverse test and quantum analogue of classical fidelity and generalized fidelity

Authors
  • Matsumoto, Keiji
Type
Preprint
Publication Date
Aug 22, 2010
Submission Date
Jun 02, 2010
Source
arXiv
License
Yellow
External links

Abstract

The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the upperbound and the lowerbund of D^{Q}({\rho}||{\sigma}) is D^{R}({\rho}||{\sigma}):=tr{\rho}ln{\sigma}^{1/2}{\rho}^{-1}{\sigma}^{1/2} and D({\rho}||{\sigma}):= tr{\rho}(ln{\rho}-ln{\sigma}), respectively. In the latter setting, we prove uniqueness of quantum relative entropy, that is, D^{Q}({\rho}||{\sigma}) should equal a constant multiple of D({\rho}||{\sigma}). In the analysis, we define and use reverse test and asymptotic reverse test, which are natural inverse of hypothesis test.

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