Reverse test and quantum analogue of classical fidelity and generalized fidelity
arXiv:1006.0302
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}(ρ||σ) is D^{R}(ρ||σ):=trρlnσ^{1/2}ρ^{-1}σ^{1/2} and D(ρ||σ):= trρ(lnρ-lnσ), respectively. In the latter setting, we prove uniqueness of quantum relative entropy, that is, D^{Q}(ρ||σ) should equal a constant multiple of D(ρ||σ). In the analysis, we define and use reverse test and asymptotic reverse test, which are natural inverse of hypothesis test.
A new proof of joint convexity of is added. Also, some technical correction, Title changed