  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.
