Group actions and Monotone Quantum Metric Tensors

TL;DR

This paper explores the relationship between Lie group actions and monotone quantum metric tensors on faithful quantum states, extending recent research in quantum information geometry.

Contribution

It advances the understanding of how Lie group actions interact with monotone quantum metrics on finite-level quantum states.

Findings

Extended the theoretical framework connecting Lie groups and quantum metrics.

Provided new insights into the geometric structure of quantum state spaces.

Clarified the role of symmetries in quantum information geometry.

Abstract

The interplay between actions of Lie groups and monotone quantum metric tensors on the space of faithful quantum states of a finite-level system observed recently in DOI: 10.1140/epjp/s13360-020-00537-y and DOI: 10.1007/978-3-030-80209-7_17 is here further developed.