Revisiting weak measurement in light of thermodynamics

TL;DR

This paper explores the thermodynamic implications of weak measurements using a von Neumann interaction, revealing how Maxwell's demon can extract information and amplify temperature, with potential realization in atomic systems.

Contribution

It introduces a thermodynamic perspective to weak measurements with a specific interaction, linking information theory and temperature amplification, and proposes a physical realization in atomic systems.

Findings

Maxwell's demon acts as a post-selection measure in weak measurement.

The von Neumann entropy difference relates to quantum-classical mutual information.

Weak value amplification can increase the system's temperature.

Abstract

We investigate a weak measurement described by a von Neumann type interaction $\hat{A}\otimes \hat{p}^2$, where $\hat{A}$ is a system observable and $\hat{p}^2$ is a measurement pointer observable. We consider the weak measurement in terms of thermodynamics by adopting a mixed Gaussian state as a quantum state of the measurement pointer. We show that Maxwell's demon appears as a measure who carries out post-selections. It is found that, even if the demon only knows the weak value, a difference in the von Neumann entropy between the initial and final system can be the QC mutual information contents, which is the maximum amount of obtainable information by a measurement. Besides, our study indicates that a temperature of the system described by this interaction is amplified by weak value amplification. In addition, we show that this demon can be realized in an atomic system.