On the Multiplicity of Density Operator Representation

TL;DR

This paper investigates the multiple ways to represent density operators in quantum mechanics, focusing on their factorizations and minimal size using novel matrix analysis techniques.

Contribution

It introduces a new matrix analysis approach to explore the multiplicity of density factor representations and identifies the minimal size density factor.

Findings

Established the existence of multiple density factors for a given density operator.

Derived the minimal size density factor using matrix analysis.

Provided a novel analytical framework not previously available.

Abstract

The density operator is usually defined starting from a set of kets in the Hilbert space and a probability distribution. From this definition it is easy to obtain a factorization of a given density operator, here called density factor (DF). The multiplicity and the variety of DFs is investigated using the tools of Matrix Analysis, arriving in particular to establish the DF with minimal size. The approach based on Matrix Analysis does not seem to be available elsewhere.