Quasi-determinism of weak measurement statistics: Laplace's demon's quantum cousin

TL;DR

This paper explores how weak measurement statistics in quantum mechanics reveal a form of quasi-determinism, resembling Laplace's demon, by examining the cancellations of uncertainties and their implications for causality.

Contribution

It analyzes the relationship between quantum measurement statistics and classical determinism, highlighting the role of weak values and uncertainties in quantum causality.

Findings

Weak measurements show zero average uncertainties for pure states.

Quantum cancellations of uncertainties mimic classical determinism.

Analysis suggests a nuanced link between quantum statistics and causality.

Abstract

Weak measurements can provide a complete characterization of post-selected ensembles, including the uncertainties of observables. Interestingly, the average uncertainties for pure initial and final states are always zero, suggesting the kind of complete knowledge that would allow a knowledge of past, presence and future in the sense of Laplace's demon. However, the quantum version actually describes cancellations of positive and negative uncertainties made possible by the strangeness of weak values. In this paper, I take a closer look at the relation between statistics and causality in quantum mechanics, in an attempt to recover the traces of classical determinism in the statistical relations of quantum measurement outcomes.