Direct experimental test of commutation relation via weak value

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.

arXiv comment8 pages, 6 figures

References in corpus (29)

• Direct Measurement of the Quantum Wavefunction
• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Quantum weak values
• Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
• Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin-measurements
• Proof of Heisenberg's error-disturbance relation
• Anomalous Weak Values Are Proofs of Contextuality
• Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values
• Quantum root-mean-square error and measurement uncertainty relations
• Quantum Cheshire Cats
• Observation of a quantum Cheshire Cat in a matter wave interferometer experiment
• The past of a quantum particle
• How well can one jointly measure two incompatible observables on a given quantum state?
• Experimental demonstration of bosonic commutation relation via superpositions of quantum operations on thermal light fields
• Noise and disturbance in quantum measurements: an information-theoretic approach
• Quantum Advantage in Postselected Metrology
• The significance of the imaginary part of the weak value
• Extracting joint weak values with local, single-particle measurements
• Approaching quantum-limited metrology with imperfect detectors by using weak-value amplification
• Measuring incompatible observables of a single photon
• Physical content of Heisenberg's uncertainty relation: Limitation and reformulation
• Experimental demonstration of direct path state characterization by strongly measuring weak values in a matter-wave interferometer
• Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements
• General complex Spin Weak Values obtained in Matter-Wave Interferometer Experiments
• Multifold paths of neutrons in the three-beam interferometer detected by tiny energy-kick
• Measuring average of non-Hermitian operator with weak value in a Mach-Zehnder interferometer
• Experimental verification of the commutation relation for Pauli spin operators using single-photon quantum interference
• Experimental test of an entropic measurement uncertainty relation for arbitrary qubit observables

Cited by in corpus (4)

• Violation of a Leggett-Garg inequality using ideal negative measurements in neutron interferometry
• Association between quantum paradoxes based on weak values and a realistic interpretation of quantum measurements
• No-go result for quantum postselection measurements of rank-m degenerate subspace
• Tight qubit uncertainty relations studied through weak values in neutron interferometry