Direct experimental test of commutation relation via imaginary weak value

The canonical commutation relation is the hallmark of quantum theory and Heisenberg's uncertainty a direct consequence it. But despite its fundamental role in theory, surprisingly, genuine experimental test has hitherto not been performed. In this article, we present novel scheme to directly between two dichotomic observables, by exploiting notion weak measurement. imaginary part suitably formulated value enables test. measurement path-qubit observable neutron interferometer experiment used verify approach. realized using newly developed technique our interferometric setup where neutron's spin/energy degree freedom serves as ancilla.