The quantum measurement process: an exactly solvable model

TL;DR

This paper presents an exactly solvable quantum measurement model that unifies quantum and classical measurement processes, demonstrating how a quantum system's state collapses into a classical outcome through unitary evolution and bath interaction.

Contribution

It introduces a detailed, solvable model of quantum measurement that explicitly shows the transition from quantum superposition to classical states via system-bath dynamics.

Findings

Measurement collapse occurs on a timescale of 1/fN due to unitary evolution.

The bath ensures the definiteness of the measurement outcome.

The resulting state is a classical mixture with a diagonal density matrix.

Abstract

An exactly solvable model for a quantum measurement is discussed, that integrates quantum measurements with classical measurements. The z-component of a spin-1/2 test spin is measured with an apparatus, that itself consists of magnet of N spin-1/2 particles, coupled to a bath. The initial state of the magnet is a metastable paramagnet, while the bath starts in a thermal, gibbsian state. Conditions are such that the act of measurement drives the magnet in the up or down ferromagnetic state, according to the sign of s_z of the test spin. The quantum measurement goes in two steps. On a timescale 1/\sqrt{N} the collapse takes place due to a unitary evolution of test spin and apparatus spins; on a larger but still short timescale this collapse is made definite by the bath. Then the system is in a `classical' state, having a diagonal density matrix. The registration of that state is basically a classical process, that can already be understood from classical statistical mechanics.