Infinite Dimensional Quantum Information Geometry

TL;DR

This paper constructs an infinite-dimensional quantum information geometric framework on a Hilbert space, introducing a Banach manifold of quantum states with a flat exponential connection, expanding the mathematical tools for quantum state analysis.

Contribution

It introduces a novel infinite-dimensional Banach manifold of quantum states with a flat exponential connection, advancing the geometric understanding of quantum information.

Findings

Constructed an infinite-dimensional Banach manifold of quantum states.

Defined a flat exponential connection on the manifold.

Discussed potential for dual mixture connection introduction.

Abstract

We present the construction of an infinite dimensional Banach manifold of quantum mechanical states on a Hilbert space H using different types of small perturbations of a given Hamiltonian. We provide the manifold with a flat connection, called the exponential connection, and comment on the possibility of introducing the dual mixture connection.