Informational steady-states and conditional entropy production in continuously monitored systems: the case of Gaussian systems

TL;DR

This paper explores how continuous measurements influence the thermodynamics and irreversibility of Gaussian quantum systems, providing a comprehensive framework to analyze informational and thermodynamic quantities in such settings.

Contribution

It develops a new toolbox for characterizing the thermodynamics of continuously measured Gaussian systems, extending previous models to include Gaussian states and processes.

Findings

Characterizes the thermodynamics of Gaussian systems under continuous measurement

Links informational quantities to entropy production and irreversibility

Provides insights relevant to recent mesoscopic quantum experiments

Abstract

The act of measuring a system has profound consequences of dynamical and thermodynamic nature. In particular, the degree of irreversibility ensuing from a non-equilibrium process is strongly affected by measurements aimed at acquiring information on the state of a system of interest: the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open system's dynamics, are related to each other by clearly interpreted informational quantities. Building on a recently proposed collisional-model framework [G. T. Landi {\it et al.}, arXiv:2103.06247], we investigate the case of continuous-variable information carriers prepared in Gaussian states and undergoing Gaussian processes. We build up a toolbox that fully characterizes the thermodynamics of continuously measured non-equilibrium Gaussian systems and processes, illustrating how the instruments hereby introduced provide key insight into recent experiments on mesoscopic quantum systems [Phys. Rev. Lett, {\bf 125}, 080601 (2020)].