Reverse test and quantum analogue of classical fidelity and generalized fidelity

Details Reverse test and quantum analogue of classical fidelity and generalized fidelity Reverse test and quantum analogue of classical fidelity and generalized fidelity

2010-06-02

arxiv.org/abs/1006.0302v3

Physics

Quantum Physics

A new proof of joint convexity of $D^R$ is added. Also, some technical correction, Title changed

Scientific paper

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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