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Updated: Aug 6, 2026
07:56
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 represented universally using chi-squared mixtures, identifying chi-squared contrasts as fundamental building blocks. This leads to a quantum thermodynamic uncertainty relation connecting state distinguishability to observable statistics.
Area of Science:
- Quantum Information Theory
- Quantum Thermodynamics
- Mathematical Physics
Background:
- Quantum states' distinguishability is quantified by f-divergences.
- Operator-convex functions define a broad class of quantum f-divergences.
Purpose of the Study:
- To establish a universal representation for quantum f-divergences.
- To derive a quantum thermodynamic uncertainty relation.
Main Methods:
- Utilizing the operator convexity of generator functions 'f'.
- Employing a universal chi-squared mixture representation.
- Mapping quantum chi-squared contrasts to classical Pearson chi-squared.
- Leveraging the Chapman-Robbins variational representation.
Main Results:
- Any Petz f-divergence admits a universal chi-squared mixture representation.
- Chi-squared contrasts are identified as atomic building blocks for quantum f-divergences.
- Closed-form weights w_f are derived for canonical f-divergences.
- A tight and universal quantum thermodynamic uncertainty relation is established.
Conclusions:
- The chi-squared mixture representation provides a unified framework for quantum f-divergences.
- The derived uncertainty relation connects quantum state distinguishability with observable statistics (mean and variance).
- This framework unifies and extends previous results in quantum thermodynamics.
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