Computing the Entropy of a Large Matrix

TL;DR

This paper presents an efficient numerical algorithm for approximating the entropy of large real symmetric positive semidefinite matrices, with an application demonstrated in quantum optics.

Contribution

The paper introduces a novel efficient method for approximating matrix entropy, specifically tailored for large matrices, with demonstrated application in quantum optics.

Findings

The new algorithm efficiently computes matrix entropy for large matrices.

Application to quantum optics validates the method's practical utility.

The approach improves computational speed over existing methods.

Abstract

Given a large real symmetric, positive semidefinite m-by-m matrix, the goal of this paper is to show how a numerical approximation of the entropy, given by the sum of the entropies of the individual eigenvalues, can be computed in an efficient way. An application from quantum-optics illustrates the new algorithm.