Coarse Quantum Measurement: An analysis of the Stern Gerlach experiment

TL;DR

This paper analyzes how limited resolution in position measurements within a Stern-Gerlach experiment affects the quantum measurement process, showing that coarse detection causes pure states to appear mixed and quantifies information gain about spin.

Contribution

It introduces a quantum-mechanical analysis of measurement coarseness in the Stern-Gerlach experiment, highlighting the impact of limited resolution on state purity and information extraction.

Findings

Coarse position detection causes pure states to appear mixed.

The analysis quantifies information gained from coarse measurements.

The approach uses a Wigner matrix to model the effects.

Abstract

We study the Quantum Measurement Process in a Stern-Gerlach setup with the spin of a silver atom as the quantum system and the position as the apparatus. The system and the apparatus are treated quantum-mechanically using unitary evolution. The new ingredient in our analysis is the idea that the probes determining the position of the silver atom are limited in resolution. We show using a Wigner matrix that due to the coarseness of the detection process, the pure density matrix appears to evolve to an impure one. We quantify the information gained about the spin in a coarse position measurement.