# Quantum Weak Values and the “Which Way?” Question

## TL;DR

The paper explores how quantum systems' paths cannot be determined without affecting their behavior, even with weak measurements.

## Contribution

It introduces the concept that weak measurements still lose individual trial information but can reveal ensemble characteristics.

## Key findings

- Weak pointers cannot determine individual quantum paths without destroying interference.
- Inaccurate quantum meters also fail to track classical systems' paths in individual trials.
- Statistical relations between probabilities or amplitudes can still be determined in both cases.

## Abstract

The 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.