Quantum fidelity for arbitrary Gaussian states

TL;DR

This paper presents a new analytical formula for quantum fidelity between any two multimode Gaussian states, facilitating advanced analysis in quantum information processing and metrology.

Contribution

It introduces a simple, computable formula for quantum fidelity of multimode Gaussian states expressed via their moments and symplectic invariants.

Findings

Derived a closed-form formula for quantum fidelity between Gaussian states

Enabled computation of Bures metric and quantum Fisher information for multimode states

Facilitated analysis of continuous-variable quantum protocols

Abstract

We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.