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.
Jensen’s inequality for operators and L¨ owner’s theorem,
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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.