Experimental weak measurement of two non-commuting observables

TL;DR

This paper reports an experimental implementation of simultaneous weak measurements of two non-commuting quantum observables using a photonic setup, revealing counter-intuitive non-monotonic information gain.

Contribution

It demonstrates a practical method for weakly measuring two non-commuting observables simultaneously with photonic systems.

Findings

Weak measurements can reveal more information than stronger measurements.

Experimental validation of simultaneous measurement of non-commuting observables.

Observation of non-monotonic information gain in weak measurements.

Abstract

The fact that not all quantum observables are jointly measurable is one of the major differences between quantum and classical theory. In the former, non-commuting observables can only be simultaneously measured with limited precision. We report on an experimental implementation of such a simultaneous measurement of two non-commuting observables based on the framework of weak von Neumann measurements. We use a photonic setup where the polarisation degree of freedom acts as the system and the two components of the transversal position correspond to the pointers of the measurement apparatuses. In addition, the theory shows that these weak measurements demonstrate a counter-intuitive non-monotonicity: weaker measurements can potentially reveal more information than stronger ones.