The canonical commutation relation is the hallmark of quantum theory and Heisenberg's uncertainty relation is a direct consequence of it. But despite its fundamental role in quantum theory, surprisingly, its genuine direct experimental test has hitherto not been performed. In this article, we present a novel scheme to directly test the canonical commutation relation between two dichotomic observables, by exploiting the notion of weak measurement. The imaginary part of a suitably formulated weak value enables this direct test. The measurement of the weak value of a path-qubit observable in a neutron interferometer experiment is used to verify the approach. The experiment is realized using a newly developed technique in our neutron interferometric setup where the neutron's spin/energy degree of freedom serves as ancilla.
Cite
@article{arxiv.2012.08171,
title = {Direct experimental test of commutation relation via weak value},
author = {Richard Wagner and Wenzel Kersten and Armin Danner and Hartmut Lemmel and Alok Kumar Pan and Stephan Sponar},
journal= {arXiv preprint arXiv:2012.08171},
year = {2021}
}