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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
Universal thermodynamic uncertainty relation for quantum f divergences
1Universidade Federal Rural de Pernambuco, Unidade de Educação a Distância e Tecnologia, 52171-900 Recife, Pernambuco, Brazil.
Abstract:
We show that any Petz f divergence (where f is operator convex) between quantum states admits a universal χ^{2}-mixture representation: the distinguishability of ρ from σ is obtained as a positive superposition of quadratic contrasts χ_{λ}^{2}, with non-negative weights w_{f}(λ) determined explicitly from the Stieltjes representation of the generator f. This identifies χ_{λ}^{2} as atomic building blocks for quantum f divergences and yields closed-form w_{f} for canonical choices (relative entropy/Kullback-Leibler, Hellinger/Bures, Rényi). By mapping χ_{λ}^{2} into a classical Pearson χ^{2}, we leverage the Chapman-Robbins variational representation and obtain a tight and universal quantum thermodynamic uncertainty relation: any f divergence is lower bounded by a function of the statistics of quantum observables (mean and variance), reproducing previous results in quantum thermodynamics as applications.
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