A limit formula for the quantum fidelity

TL;DR

This paper introduces a limit formula for quantum fidelity between mixed and pure states, simplifying calculations especially for multimode Gaussian states by expressing fidelity in terms of their statistical moments.

Contribution

The paper presents a novel limit formula for quantum fidelity applicable to mixed and pure states, with a specific application to multimode Gaussian states.

Findings

Derived a limit formula for quantum fidelity.

Applied the formula to multimode Gaussian states.

Obtained a simple expression in terms of statistical moments.

Abstract

Quantum fidelity is a central tool in quantum information, quantifying how much two quantum states are similar. Here we propose a limit formula for the quantum fidelity between a mixed state and a pure state. As an example of an application, we apply this formula to the case of multimode Gaussian states, achieving a simple expression in terms of their first and second-order statistical moments.