Unfolding of relative g-entropies and monotone metrics

TL;DR

This paper explores the geometric structure of quantum information metrics by analyzing the unfolding of relative g-entropies, revealing new insights into quantum monotone metrics and their tensor representations.

Contribution

It introduces a geometric unfolding approach to quantum information metrics, clarifying the form of monotone tensors and their relation to relative g-entropies.

Findings

Unveiled the geometric structure of quantum monotone metrics in unfolding space

Connected relative g-entropies with covariant tensor extraction methods

Provided a new perspective on quantum information geometry

Abstract

We discuss the geometric aspects of a recently described unfolding procedure and show the form of objects relevant in the field of Quantum Information Geometry in the unfolding space. In particular, we show the form of the quantum monotone metric tensors characterized by Petz and retrace in this unfolded perspective a recently introduced procedure of extracting a covariant tensor from a relative $g$-entropy.