Escort density operators and generalized quantum information measures

TL;DR

This paper introduces escort density operators and phi-exponential families to generalize quantum information measures, establishing bounds, entropy principles, and thermodynamic structures in quantum systems.

Contribution

It proposes a novel framework involving escort density operators and phi-exponential families for generalized quantum information measures and bounds.

Findings

Generalized lower bound involving escort density operators

Introduction of phi-exponential family and its properties

Thermodynamic structure with entropy and free energy relations

Abstract

Parametrized families of density operators are studied. A generalization of the lower bound of Cramer and Rao is formulated. It involves escort density operators. The notion of phi-exponential family is introduced. This family, together with its escort, optimizes the generalized lower bound. It also satisfies a maximum entropy principle and exhibits a thermodynamic structure in which entropy and free energy are related by Legendre transform.