Optimal purifications and fidelity for displaced thermal states

TL;DR

This paper derives the maximum fidelity between two displaced thermal states by identifying optimal two-mode displaced Gaussian purifications, providing a precise measure of their similarity in quantum information.

Contribution

It establishes the form of optimal purifications for displaced thermal states and calculates their fidelity, advancing understanding of quantum state overlaps.

Findings

Optimal purifications are two-mode displaced Gaussian states.

Derived explicit formula for fidelity between displaced thermal states.

Enhanced methods for quantum state comparison and fidelity estimation.

Abstract

We evaluate the Uhlmann fidelity between two one-mode displaced thermal states as the maximal probability transition between appropriate purifications of the given states. The optimal purifications defining the fidelity are proved to be two-mode displaced Gaussian states.