Tight qubit uncertainty relations studied through weak values in neutron interferometry
arXiv:2505.22221 · doi:10.1103/pthn-81pm
Abstract
In its original formulation, Heisenberg's uncertainty principle describes a trade-off relation between the error of a quantum measurement and the thereby induced disturbance on the measured object. However, this relation is not valid in general. An alternative universally valid relation was derived by Ozawa in 2003, defining error and disturbance in a general concept, experimentally accessible via a tomographic method. Later, it was shown by Hall that these errors correspond to the statistical deviation between a physical property and its estimate. Recently, it was discovered that these errors can be observed experimentally when weak values are determined through a procedure named "feedback compensation". Here, we apply this procedure for the complete experimental characterization of the error-disturbance relation between a which-way observable in an interferometer and another observable associated with the output of the interferometer, confirming the theoretically predicted relation. As expected for pure states, the uncertainty is tightly fulfilled.
10 pages, 8 figures
References in corpus (17)
- Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
- Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin-measurements
- Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
- Proof of Heisenberg's error-disturbance relation
- Quantum root-mean-square error and measurement uncertainty relations
- How well can one jointly measure two incompatible observables on a given quantum state?
- Prior information: how to circumvent the standard joint-measurement uncertainty relation
- Noise and disturbance in quantum measurements: an information-theoretic approach
- Joint quantum measurements with minimum uncertainty
- Heisenberg uncertainty for qubit measurements
- Measuring measurement--disturbance relationships with weak values
- Uncertainty limits for quantum metrology obtained from the statistics of weak measurements
- Measurement uncertainty relations for discrete observables: Relative entropy formulation
- Quantifying the presence of a neutron in the paths of an interferometer
- Error-Disturbance Trade-off in Sequential Quantum Measurements
- Direct evaluation of measurement uncertainties by feedback compensation of decoherence
- Direct experimental test of commutation relation via weak value