Quantum fidelity for Gaussian states describing the evolution of open systems

TL;DR

This paper investigates how quantum fidelity evolves over time for Gaussian states of a harmonic oscillator interacting with a thermal environment, providing insights into the effects of initial state parameters and bath conditions.

Contribution

It introduces a comprehensive analysis of quantum fidelity dynamics for Gaussian states in open systems, considering various initial states and environmental parameters.

Findings

Quantum fidelity depends on initial squeezing and correlations.

Fidelity decreases over time due to dissipation and thermal effects.

The study provides explicit formulas for fidelity evolution in open quantum systems.

Abstract

Using the expression of the fidelity for the most general Gaussian quantum states, the quantum fidelity is studied for the states of a harmonic oscillator interacting with an environment, in particular with a thermal bath. The time evolution of the considered system is described in the framework of the theory of open systems based on quantum dynamical semigroups. By taking a correlated squeezed Gaussian state as initial state, we calculate the quantum fidelity for both undisplaced and displaced states. The time evolution of the quantum fidelity is analyzed depending on the squeezing and correlation parameters characterizing the initial Gaussian state and on the dissipation constant and temperature of the thermal bath.