The quantum information manifold for epsilon-bounded forms

TL;DR

This paper establishes that under certain conditions, the free energy and associated density operators form an analytic manifold in the context of quantum information theory, extending the understanding of perturbations in quantum systems.

Contribution

It introduces a new framework for analyzing the analyticity of free energy and density operators under epsilon-bounded form perturbations of self-adjoint operators.

Findings

Free energy is analytic in the perturbation V.

Density operators form an analytic manifold.

Results apply to Gibbs states with sufficient regularity.

Abstract

Let H be a self-adjoint operator bounded below by 1, and let V be a small form perturbation such that RVS has finite norm, where R is the resolvent at zero to the power 1/2 +epsilon, and S is the resolvent to the power 1/2-epsilon. Here, epsilon lies between 0 and 1/2. If the Gibbs state defined by H is sufficiently regular, we show that the free energy is an analytic function of V in the sense of Frechet, and that the family of density operators defined in this way is an analytic manifold modelled on a Banach space.