Geodesic distances on density matrices

TL;DR

This paper establishes an upper bound for geodesic distances derived from monotone Riemannian metrics on positive definite and density matrices, contributing to quantum information geometry.

Contribution

It introduces a new upper bound for geodesic distances on density matrices within the framework of monotone Riemannian metrics.

Findings

Derived an explicit upper bound for geodesic distances

Applicable to quantum density matrices and positive definite matrices

Enhances understanding of quantum geometric structures

Abstract

We find an upper bound for geodesic distances associated to monotone Riemannian metrics on positive definite matrices and density matrices.