Non-representative quantum mechanical weak values

TL;DR

This paper investigates the conditions under which weak values in quantum mechanics do not smoothly converge to the system's undisturbed state, challenging their interpretation as properties of the system.

Contribution

It identifies scenarios where the weak measurement limit is discontinuous, showing that weak values may not always reflect the true properties of the quantum system.

Findings

Weak value limits can be discontinuous under certain conditions.

Discontinuous cases imply weak values do not represent the undisturbed system.

Examples demonstrate the non-representativeness of some weak values.

Abstract

The operational definition of a weak value for a quantum mechanical system involves the limit of the weak measurement strength tending to zero. I study how this limit compares to the situation for the undisturbed (no weak measurement) system. Under certain conditions, which I investigate, this limit is discontinuous in the sense that it does not merge smoothly to the Hilbert space description of the undisturbed system. Hence, in these discontinuous cases, the weak value does not represent the undisturbed system. As a result, conclusions drawn from such weak values regarding the properties of the studied system cannot be upheld. Examples are given.