The Role of Heat Bath and Pointer Modes in Quantum Measurement

TL;DR

This paper derives an exact model of quantum measurement involving heat bath and pointer modes, showing how strong interactions produce a statistical mixture of eigenstates with correct probabilities and amplified pointer information.

Contribution

It provides an exact derivation of the measurement process involving heat bath and pointer modes, clarifying the emergence of eigenstates and information amplification in quantum measurement.

Findings

System evolves into a mixture of eigenstates with correct probabilities

Pointer operators retain amplified information about the system

Strong interaction leads to a statistical mixture of product states

Abstract

We present an exact derivation of a process in which a microscopic measured system interacts with "heat bath" and pointer modes of a measuring device, via a linear coupling involving Hermitian operator $\Lambda$ of the system. In the limit of strong interaction with these modes, over a small time interval, we show that the measured system and the "pointer" part of the measuring device evolve into a statistical mixture of direct-product states such that the system is in each eigenstate of $\Lambda$ with the correct quantum-mechanical probability, whereas the expectation values of pointer-space operators retain amplified information of the system's eigenstate.