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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.
Physical Review. E
|July 24, 2026
Summary
Quantum f-divergences are universally represented as mixtures of quadratic contrasts. This finding establishes quantum quadratic contrasts as fundamental building blocks and reveals a universal quantum thermodynamic uncertainty relation.
Area of Science:
- Quantum Information Theory
- Quantum Thermodynamics
- Mathematical Physics
Background:
- Quantum f-divergences quantify the distinguishability between quantum states.
- Operator-convex functions define a broad class of quantum f-divergences, including important examples like relative entropy and Hellinger distance.
- Understanding the fundamental structure and properties of these divergences is crucial for quantum information processing and thermodynamics.
Purpose of the Study:
- To establish a universal representation for Petz f-divergences.
- To identify fundamental building blocks for quantum f-divergences.
- To derive a universal quantum thermodynamic uncertainty relation.
Main Methods:
- Utilizing the operator convexity of the function f.
- Employing a universal χ²-mixture representation for quantum f-divergences.
- Mapping quantum quadratic contrasts to classical Pearson χ² statistics.
- Leveraging the Chapman-Robbins variational representation.
Main Results:
- Any Petz f-divergence admits a universal χ²-mixture representation.
- Quantum quadratic contrasts (χ²λ) are identified as atomic building blocks for quantum f-divergences.
- Closed-form weights (w_f) for canonical f-divergences (relative entropy, Hellinger, Rényi) are derived.
- A tight and universal quantum thermodynamic uncertainty relation is established, bounding f-divergences by quantum observable statistics (mean and variance).
Conclusions:
- The χ²-mixture representation provides a unified framework for understanding quantum f-divergences.
- The derived quantum thermodynamic uncertainty relation generalizes previous results and highlights the fundamental connection between distinguishability and statistical fluctuations.
- This work offers new tools for analyzing quantum states and processes in various quantum applications.
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