Universal Thermodynamic Uncertainty Relation for Quantum $f-$Divergences

• URL: http://arxiv.org/abs/2511.10817v1
• Date: Thu, 13 Nov 2025 21:31:46 GMT
• Title: Universal Thermodynamic Uncertainty Relation for Quantum $f-$Divergences
• Authors: Domingos S. P. Salazar,
• Abstract summary: We show that any Petz $f$-divergence (where $f$ is operator convex) between quantum states admits a universal $2$-mixture representation.<n>This identifies $2_$ as atomic building blocks for quantum $f$-divergences and yields closed-form $w_f$ for canonical choices.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $χ^2_λ$, with nonnegative weights $w_f(λ)$ determined explicitly from the Stieltjes representation of the generator $f$. This identifies $χ^2_λ$ as atomic building blocks for quantum $f$-divergences and yields closed-form $w_f$ for canonical choices (relative entropy/KL, Hellinger/Bures, R'{e}nyi). By mapping $χ^2_λ$ 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 and novel results in quantum thermodynamics as applications.

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