Pointer-based model for state reduction in momentum space

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.

Qubit-based momentum measurement of a particle

“…In a previous work [26] it was shown that the momentum of a free, non-relativistic quantum particle can be extracted from an operational observable based on the concept of a classical ToF measurement. This observable has been defined with the help of two continuous systems, serving as pointers in the sense of von Neumann.…”