Fidelity of states in infinite dimensional quantum systems

TL;DR

This paper explores the concept of fidelity in infinite dimensional quantum systems, providing an elementary proof of Uhlmann's theorem extension and generalizing key properties from finite to infinite dimensions, revealing some differences.

Contribution

It offers an elementary proof of the infinite dimensional Uhlmann's theorem and extends fidelity properties to infinite dimensional quantum systems, highlighting differences from finite cases.

Findings

Extended fidelity properties to infinite dimensions

Provided an elementary proof of Uhlmann's theorem in infinite dimensions

Identified differences from finite-dimensional fidelity properties

Abstract

In this paper we discuss the fidelity of states in infinite dimensional systems, give an elementary proof of the infinite dimensional version of Uhlmann's theorem, and then, apply it to generalize several properties of the fidelity from finite dimensional case to infinite dimensional case. Some of them are somewhat different from those for finite dimensional case.