Dynamics of ideal quantum measurement of a spin 1 with a Curie-Weiss magnet

TL;DR

This paper analyzes the dynamical process of ideal quantum measurement for a spin-1 system using a Curie-Weiss magnet model, extending previous spin-1/2 models and evaluating energy costs numerically.

Contribution

It provides a detailed dynamical solution for measuring a spin-1 system's z-component, extending the Curie-Weiss measurement model beyond spin-1/2.

Findings

Dynamical equations for spin-1 measurement are solved and numerically evaluated.

Energy costs of the measurement process are quantified.

The model's generalization to higher spins is straightforward.

Abstract

Quantum measurement is a dynamical process of an apparatus coupled to a test system. Ideal measurement of the $z$-component of a spin-$\frac{1}{2}$ ($s_z=\pm\frac{1}{2}$) has been modeled by the Curie-Weiss model for quantum measurement. Recently, the model was generalized to higher spin and the thermodynamics was solved. Here the dynamics is considered. To this end, the dynamics for spin-$\frac{1}{2}$ case are cast in general notation. The dynamics of the measurement of the $z$-component of a spin-1 ($s_z=0,\pm 1$) are solved in detail and evaluated numerically. Energy costs of the measurement, which are macroscopic, are evaluated. Generalization to higher spin is straightforward.