Group actions and monotone metric tensors: The qubit case

TL;DR

This paper explores the relationship between group actions and monotone metric tensors specifically for qubits, providing a comprehensive analysis of this connection in quantum information geometry.

Contribution

It offers a complete discussion of how group actions relate to monotone metric tensors in the context of qubits, extending previous partial results.

Findings

Established a detailed link between group actions and monotone metrics for qubits

Provided a classification of monotone metric tensors under group symmetries

Enhanced understanding of quantum state space geometry for two-level systems

Abstract

In recent works, a link between group actions and information metrics on the space of faithful quantum states has been highlighted in particular cases. In this contribution, we give a complete discussion of this instance for the particular case of the qubit.