Pointer-based model for state reduction in momentum space

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. Graphical abstract