A Note Concerning von Neumann Projector Measurement Pointer States, Weak Values, and Interference

TL;DR

This paper explores how pointer states in von Neumann measurements depend on weak values and pre/postselection, revealing interference effects and the role of welcher Weg information in quantum measurements.

Contribution

It demonstrates that pointer states depend on weak values regardless of measurement strength and explains interference phenomena through welcher Weg information.

Findings

Pointer states depend on weak values with pre/postselection.

Interference occurs in postselected pointer states but not in initial states.

Interference is linked to welcher Weg information.

Abstract

It is well known that the pointer state |{\Phi}> resulting from the von Neumann measurement of a projection operator A performed upon an ensemble of quantum systems in the preselected state |{\psi}> depends upon A|{\psi}>. Here it is shown that the pointer state |{\Psi}> obtained from such a measurement performed upon an ensemble that is also postselected depends upon the weak value of A - regardless of the measurement interaction strength. It is also found that, while the spatial distribution of |{\Psi}> exhibits interference, the idempotency of A prohibits interference in that of |{\Phi}>. This is explained in terms of welcher Weg information.