Pointer-based model for state reduction in momentum space

TL;DR

This paper introduces a pointer-based quantum measurement model for momentum in the momentum space, demonstrating how single measurements induce state reduction and operationally define momentum via a time-of-flight observable.

Contribution

It develops a Hamiltonian-based framework for quantum pointers to measure momentum, extending von Neumann's measurement concept to a new operational context.

Findings

Single measurements cause state reduction downstream.

The model defines a quantum time-of-flight observable for momentum.

The approach links measurement dynamics with momentum state reduction.

Abstract

We revisit the pointer-based measurement concept of von Neumann which allows us to model a quantum counterpart of the classical time-of-flight (ToF) momentum. Our approach is based on the Hamiltonian for a particle interacting with two quantum pointers serving as basic measurement devices. The corresponding dynamics leads to a pointer-based ToF observable for the operational momentum of the particle. We can consider single measurements of our quantum pointers and show that this process will result in a state reduction for a single particle being downstream of the time-of-flight setup.