Daemonic ergotropy of Gaussian quantum states and the role of measurement-induced purification via general-dyne detection

TL;DR

This paper investigates the maximum work extractable from Gaussian quantum states using measurement-assisted protocols, revealing how measurement-induced purification enhances daemonic ergotropy and providing explicit strategies for optimal work extraction.

Contribution

It derives a general expression for daemonic ergotropy in Gaussian systems and links it to measurement-induced purification, with practical examples demonstrating optimal strategies.

Findings

Daemonic ergotropy depends only on energy and purity for single-mode Gaussian states.

Measurement-induced purification directly enhances the potential for work extraction.

Optimal measurement strategies maximize conditional purity and daemonic ergotropy.

Abstract

According to the Maxwell demon paradigm, additional work can be extracted from a classical or quantum system by exploiting information obtained through measurements on a correlated ancillary system. In the quantum setting, the maximum work extractable via unitary operations in such measurement-assisted protocols is referred to as daemonic ergotropy. In this work, we explore this concept in the context of continuous-variable quantum systems, focusing on Gaussian states and general-dyne (Gaussian) measurements. We derive a general expression for the daemonic ergotropy and examine two key scenarios: (i) bipartite Gaussian states where a general-dyne measurement is performed on one of the two parties, and (ii) open Gaussian quantum systems under continuous general-dyne monitoring of the environment. Remarkably, we show that for single-mode Gaussian states, the ergotropy depends solely on the state's energy and purity. This enables us to express the daemonic ergotropy as a simple function of the unconditional energy and the purity of the conditional states, revealing that enhanced daemonic work extraction is directly linked to measurement-induced purification. We illustrate our findings through two paradigmatic examples: extracting daemonic work from a two-mode squeezed thermal state and from a continuously monitored optical parametric oscillator. In both case we identify the optimal general-dyne strategies that maximize the conditional purity and, in turn, the daemonic ergotropy.