Monotone metric tensors in Quantum Information Geometry

TL;DR

This paper reviews the geometric properties of monotone quantum metrics in finite-dimensional quantum information theory, emphasizing a spectral theorem-based perspective to compare quantum and classical probability geometries.

Contribution

It introduces an unfolded spectral perspective for quantum states to analyze monotone metrics and their relation to classical probability geometries.

Findings

Highlights geometric features of monotone quantum metrics

Provides a spectral theorem-based framework for quantum state analysis

Facilitates comparison between quantum and classical probability geometries

Abstract

We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem and is naturally suited to investigate the comparison with the classical case of probability distributions.