Bayes' rule, generalized discord, and nonextensive thermodynamics

TL;DR

This paper develops generalized quantum correlation measures based on Bayes' rule, linking them to nonextensive thermodynamics and providing an operational interpretation through work extraction differences.

Contribution

It introduces a unified framework for quantum correlation measures using Bayes' rule and connects them with nonextensive thermodynamics and generalized discord.

Findings

Derived quantum correlation measures satisfy key conditions.

Established operational interpretation via work extraction efficiency.

Unified entropic and geometric discord measures within nonextensive thermodynamics.

Abstract

Generalized measures of quantum correlations are derived by taking Bayes' rule as the only fundamental principle. The resulting quantifiers satisfy several desirable conditions for a measure of quantum correlations and are shown to admit operational interpretation in terms of the difference in efficiency of quantum and classical demons in allowing for the extraction of generalized work from a heat bath. The link with discord is established by adopting the $q$ entropy as entropic principle. This allows us to reproduce, within a one-parameter formalism, both the entropic and the geometric measures of discord and physically distinguish them within the context of the nonextensive thermodynamics. Besides offering a unified view of several measures of correlations in terms of the Bayesian principle and its connection with thermodynamics, our approach unveils a bridge to the nonextensive statistical mechanics.