Symmetric Logarithmic Derivative of Fermionic Gaussian States

Angelo Carollo; Bernardo Spagnolo; Davide Valenti

doi:10.3390/e20070485

Symmetric Logarithmic Derivative of Fermionic Gaussian States

Entropy (Basel). 2018 Jun 22;20(7):485. doi: 10.3390/e20070485.

Authors

Angelo Carollo^{1

2}, Bernardo Spagnolo^{1

2

3}, Davide Valenti^{1

4}

Affiliations

¹ Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, Palermo University and CNISM, Viale delle Scienze, Ed. 18, I-90128 Palermo, Italy.
² Department of Radiophysics, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni Novgorod 603950, Russia.
³ Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-90123 Catania, Italy.
⁴ Istituto di Biomedicina ed Immunologia Molecolare (IBIM) "Alberto Monroy", CNR, Via Ugo La Malfa 153, I-90146 Palermo, Italy.

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 range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.

Keywords: Fermionic Gaussian state; quantum geometric information; quantum metrology.