Manifold of density matrices

TL;DR

This paper explores the geometric structure of the manifold of density matrices, showing it can be derived from complex projective space via the action of the special unitary group SU(N).

Contribution

It introduces a new geometric perspective on density matrices by relating them to complex projective space and SU(N) actions, providing foundational insights.

Findings

Density matrices form a manifold derived from CP^{N^2-1}

SU(N) acts on this manifold to generate density matrices

Preliminary observations on the manifold's structure are provided

Abstract

We show that the manifold of density matrices can be derived from CP^{N^2-1} by the action of SU(N). We give some preliminary observations on the structure of this manifold.