Quantum Fisher information on two manifolds of two-mode Gaussian states

TL;DR

This paper analyzes the geometric and statistical properties of two classes of two-mode Gaussian states, focusing on quantum Fisher information, fidelity, and Bures metric curvature to enhance understanding of parameter estimation in quantum optics.

Contribution

It provides explicit formulas for fidelity and quantum Fisher information matrices for mode-mixed and squeezed thermal states, and evaluates their Bures metric curvatures, linking geometry with quantum statistical properties.

Findings

Quantum Fisher information matrices are diagonal for both classes.

Scalar curvatures depend on mean photon numbers and reveal geometric features.

The study facilitates better parameter estimation in optical quantum states.

Abstract

We investigate two special classes of two-mode Gaussian states of light that are important from both the experimental and theoretical points of view: the mode-mixed thermal states and the squeezed thermal ones. Aiming to a parallel study, we write the Uhlmann fidelity between pairs of states belonging to each class in terms of their defining parameters. The quantum Fisher information matrices on the corresponding four-dimensional manifolds are diagonal and allow insightful parameter estimation. The scalar curvatures of the Bures metric on both Riemannian manifolds of special two-mode Gaussian states are evaluated and discussed. They are functions of two variables, namely, the mean numbers of photons in the incident thermal modes. Our comparative analysis opens the door to further investigation of the interplay between geometry and statistics for Gaussian states produced in simple optical devices.