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arXiv:2201.02578 · International Journal of Theoretical Physics

Quantifying Unsharpness of Observables in an Outcome-Independent way

Arindam Mitra

Published Sep 22, 2022• 6 citations
arXivHTMLPDF
DOI
10.1007/s10773-022-05219-2

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Multiple observers who independently harvest nonclassical correlations from a single physical system share the system's ability to enable quantum correlations. We show that any number of independent observers can share the preparation contextual outcome statistics enabled by state ensembles in quantum theory. Furthermore, we show that even in the presence of any amount of white noise, there exists quantum ensembles that enable such shared preparation contextuality. The findings are experimentally realised by applying sequential unsharp measurements to an optical qubit ensemble which reveals three shared demonstrations of preparation contextuality.
Unsharp measurements are increasingly important in quantum information theory and tests of quantum theory. Here, in a semi-device-independent setting, we experimentally demonstrate their noise-robust characterisation while only assuming that the involved devices operate on qubits and that the detected events constitute a fair sample. Our experiment involves three parties; the first party prepares a qubit system, the second party performs operations which returns both a classical and quantum outcome and the later is measured by the third party. From the measured probabilities we show nearly-optimal quantum correlations for unsharp observales, falsify every model in which the operations are simulated with stochastic projective qubit measurements and obtain narrow intervals to which the sharpness parameter can be confined. Moreover, we also certify two sequential pairs of incompatible measurements and quantify their degree of incompatibility. Finally, we discuss our characterisation of the sharpness parameter as compared to that obtained from a tomographic scheme subjected to small errors.