Quantum States, Groups and Monotone Metric Tensors

TL;DR

This paper explores the relationship between monotone metric tensors and unitary group actions on quantum states, providing illustrative examples involving key quantum metrics.

Contribution

It introduces a new connection between monotone metrics and unitary group actions on quantum state manifolds, with specific examples for well-known metrics.

Findings

Established links between monotone metrics and unitary group actions

Provided explicit examples with Bures-Helstrom, Wigner-Yanase, and Bogoliubov-Kubo-Mori metrics

Enhanced understanding of geometric structures in quantum state space

Abstract

A novel link between monotone metric tensors and actions of suitable extensions of the unitary group on the manifold of faithful quantum states is presented here by means of three illustrative examples related with the Bures-Helstrom metric tensor, the Wigner-Yanase metric tensor, and the Bogoliubov-Kubo-Mori metric tensor.