Curie-Weiss model of the quantum measurement process

TL;DR

This paper presents an exactly solved Hamiltonian model of quantum measurement, demonstrating how a macroscopic apparatus can produce measurement outcomes consistent with quantum mechanics through standard statistical mechanics.

Contribution

It introduces a realistic Hamiltonian model of quantum measurement involving a large spin system and a phase transition mechanism, showing how measurement results emerge naturally.

Findings

The apparatus acts on the system rapidly, causing state collapse.

The process involves multiple time scales and a phase transition in the apparatus.

Measurement outcomes follow Born's rule, with correlations between system and apparatus.

Abstract

A hamiltonian model is solved, which satisfies all requirements for a realistic ideal quantum measurement. The system S is a spin-$\half$, whose $z$-component is measured through coupling with an apparatus A=M+B, consisting of a magnet $\RM$ formed by a set of $N\gg 1$ spins with quartic infinite-range Ising interactions, and a phonon bath $\RB$ at temperature $T$. Initially A is in a metastable paramagnetic phase. The process involves several time-scales. Without being much affected, A first acts on S, whose state collapses in a very brief time. The mechanism differs from the usual decoherence. Soon after its irreversibility is achieved. Finally the field induced by S on M, which may take two opposite values with probabilities given by Born's rule, drives A into its up or down ferromagnetic phase. The overall final state involves the expected correlations between the result registered in M and the state of S. The measurement is thus accounted for by standard quantum statistical mechanics and its specific features arise from the macroscopic size of the apparatus.