Perturbation theory of von Neumann Entropy

TL;DR

This paper develops a systematic perturbation theory for calculating von Neumann entropy in quantum systems, including degenerate and non-degenerate cases, providing a practical expansion method for complex states.

Contribution

It introduces a novel perturbation approach to evaluate von Neumann entropy, applicable to both finite and infinite-dimensional quantum systems.

Findings

Provides a systematic perturbation framework for von Neumann entropy

Enables practical entropy calculations for complex quantum states

Applicable to continuous variable quantum systems

Abstract

In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the dimension is infinite. We develop the perturbation theory systematically for calculating von Neumann entropy of non-degenerate systems as well as degenerate systems. The result turns out to be a practical way of the expansion calculation of von Neumann entropy.