Inaccurate (weak) measurements classical and quantum

TL;DR

This paper analyzes highly inaccurate measurements in classical and quantum systems, showing that while individual trial information is lost, ensemble parameters can still be extracted, and quantum quasi-probabilities can exhibit sign changes without indicating large quantum variable values.

Contribution

It demonstrates that weak measurements in both classical and quantum contexts lead to information loss at the individual level but allow ensemble analysis, clarifying the nature of quantum quasi-probabilities.

Findings

Ensemble parameters can be extracted despite individual information loss.

Quantum quasi-probabilities can change sign, indicating distribution reshaping.

Large meter readings are due to distribution reshaping, not large quantum variables.

Abstract

We consider highly inaccurate measurements made on classical stochastic and quantum systems. In the quantum case such a \e{weak} measurement preserves coherence between the system's alternatives. We demonstrate that in both cases the information about the scenario realised in each individual trial is lost. However, ensemble parameters such as classical path probabilities, and quantum quasi-probabilities can be extracted from the obtained statistics. In both cases causality ensures that additional post-selection only redistributes individual outcomes between the system's final states. Quantum quasi-probabilities may change sign, which allows for anomalously large meter's (pointer's) reading for some final states. These, we show, result from mere \e{reshaping} of a broad distribution obtained earlier, and provide no \e{experimental evidence} of quantum variables taking, on rare occasions, exceptionally large values.