No-Go Theorem for Quantum Heat Engines Powered Purely by Quantum Measurements in the Steady Regime

TL;DR

This paper proves that quantum measurement-powered engines cannot extract work in the steady regime without feedback or thermal contact, due to measurements becoming nondisturbing and energy-neutral over time.

Contribution

It establishes a no-go theorem showing the impossibility of steady-work extraction in measurement-driven quantum engines without additional entropy-decreasing processes.

Findings

Work cannot be extracted in the steady regime of measurement-powered engines.

Quantum measurements become nondisturbing and energy-neutral over time.

Feedback control or thermal contact are necessary for work extraction.

Abstract

We study the thermodynamics of a quantum measurement-powered engine that converts energy injected by measurement backaction into work. We consider an engine with a finite-dimensional working substance, driven purely by quantum measurements, i.e., by bare quantum measurements, without feedback control or thermal contact in the thermodynamic cycle. On the basis of a Poincar\'e-like recurrence theorem for general quantum channels, we prove a no-go result for work extraction from such an engine in the steady regime. In the steady regime, quantum measurements become nondisturbing and do not inject energy into the working substance. Consequently, no work can be extracted. This result reveals the necessity of an entropy-decreasing process, such as feedback control or thermal contact, for work extraction in steady-cycle measurement-powered engines.