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arXiv · 2012.08171

Direct experimental test of commutation relation via weak value

Richard Wagner·Wenzel Kersten·Armin Danner·Hartmut Lemmel·Alok Kumar Pan·Stephan Sponar
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Abstract

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.

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Richard Wagner, Wenzel Kersten, Armin Danner, Hartmut Lemmel, Alok Kumar Pan, Stephan Sponar. 2020-12-15. Direct experimental test of commutation relation via weak value. https://doi.org/10.1103/physrevresearch.3.023243

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