Polar paths realize the interval [FM(P,Q), FU(P,Q)] yielding z-fidelities for z≥1/2 and Log-Euclidean fidelity; Holevo bases are classified and unitary factors are those W where P^{-1/2}Q^{1/2}W is similar to a positive definite matrix.
Reverse test and quantum analogue of classical fidelity and generalized fidelity
2 Pith papers cite this work. Polarity classification is still indexing.
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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.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Defines weighted spectral fidelity F_t^spec(ρ,σ) = Tr[ρ (ρ^{-1} ♯ σ)^{2t}] for t in [0,1], establishes unitary invariance, multiplicativity, concavity in each variable, and violations of DPI away from t=1/2.
citing papers explorer
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Polar Fidelities, Holevo Bases, and Unitary Factors of Generalized Fidelity
Polar paths realize the interval [FM(P,Q), FU(P,Q)] yielding z-fidelities for z≥1/2 and Log-Euclidean fidelity; Holevo bases are classified and unitary factors are those W where P^{-1/2}Q^{1/2}W is similar to a positive definite matrix.
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A Weighted Spectral Quantum Fidelity
Defines weighted spectral fidelity F_t^spec(ρ,σ) = Tr[ρ (ρ^{-1} ♯ σ)^{2t}] for t in [0,1], establishes unitary invariance, multiplicativity, concavity in each variable, and violations of DPI away from t=1/2.