Dynamics of moments of arbitrary order for stochastic Poisson squeezings

TL;DR

This paper derives explicit formulas for the evolution of moments of any order in a GKSL equation driven by Poisson processes with unitary jumps, focusing on squeeze operators.

Contribution

It provides a novel explicit characterization of moment dynamics for Poisson-driven GKSL equations involving squeeze operators.

Findings

Explicit moment dynamics formulas derived

Applicable to Poisson processes with unitary jumps

Enhances understanding of quantum stochastic processes

Abstract

The explicit dynamics of the moments for the GKSL equation is obtained. In our case the GKSL equation corresponds to Poisson stochastic processes which lead to unitary jumps. We consider squeeze operators as the unitary jumps.