Quantum weak values and the 'which way?' question

TL;DR

The paper explores the limitations of weak measurements in quantum systems, showing that they cannot reliably determine the path taken by a quantum particle due to inherent inaccuracies, and discusses similar issues in classical systems.

Contribution

It demonstrates that weak pointers are inherently inaccurate, preventing reliable path determination in quantum and classical systems, and clarifies the relation between statistical ensemble characteristics.

Findings

Weak pointers are inherently inaccurate, leading to loss of path information.

In quantum systems, weak measurements relate to probability amplitudes.

Classical systems monitored by inaccurate quantum meters exhibit similar issues.

Abstract

Uncertainty principle forbids one to determine which of the two paths a quantum system has travelled, unless interference between the alternatives had been destroyed by a measuring device, e.g., by a pointer. One can try to weaken the coupling between the device and the system, in order to avoid the veto. We demonstrate, however, that a weak pointer is at the same time an inaccurate one, and the information about the path taken by the system in each individual trial is inevitably lost. We show also that a similar problem occurs if a classical system is monitored by an inaccurate quantum meter. In both cases one can still determine some characteristic of the corresponding statistical ensemble, a relation between path probabilities in the classical case, and a relation between the probability amplitudes if a quantum system is involved.