The Infinite-Dimensional Quantum Entropy: the Unified Entropy Case

TL;DR

This paper extends the concept of unified quantum entropy to infinite-dimensional systems using Fredholm determinant theory, analyzing its properties and proposing numerical methods for computation.

Contribution

It introduces a framework for infinite-dimensional unified quantum entropy and extends known properties from finite-dimensional cases.

Findings

Extended unified quantum entropy to infinite-dimensional systems.

Analyzed basic properties of the infinite-dimensional entropy.

Outlined numerical approaches for entropy computation.

Abstract

By a use of the Fredholm determinant theory, the unified quantum entropy notion has been extended to a case of infinite-dimensional systems. Some of the known (in the finite-dimensional case) basic properties of the introduced unified entropies have been extended to the case study. Certain numerical approaches for computing the proposed finite and infinite-dimensional entropies are being outlined as well.