Symmetric Logarithmic Derivative of Fermionic Gaussian States

TL;DR

This paper derives a closed-form expression for the symmetric logarithmic derivative of Fermionic Gaussian states, enabling efficient computation of quantum Fisher Information for quantum metrology applications involving fermionic systems.

Contribution

It introduces a novel closed-form formula for the symmetric logarithmic derivative specific to Fermionic Gaussian states, facilitating quantum Fisher Information calculations.

Findings

Enables direct computation of quantum Fisher Information for Fermionic Gaussian states.

Applicable to quantum metrology with thermal and non-equilibrium steady states.

Provides a mathematical tool for analyzing fermionic many-body systems.

Abstract

In this article we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications ranges from quantum Metrology with thermal states and non-equilibrium steady states with Fermionic many-body systems.