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Journal Articles Journal of Mathematical Physics Year : 2023

Relating incompatibility, noncommutativity, uncertainty and Kirkwood-Dirac nonclassicality

Abstract

We provide an in-depth study of the recently introduced notion of completely incompatible observables and its links to the support uncertainty and to the Kirkwood-Dirac nonclassicality of pure quantum states. The latter notion has recently been proven central to a number of issues in quantum information theory and quantum metrology. In this last context, it was shown that a quantum advantage requires the use of Kirkwood-Dirac nonclassical states. We establish sharp bounds of very general validity that imply that the support uncertainty is an efficient Kirkwood-Dirac nonclassicality witness. When adapted to completely incompatible observables that are close to mutually unbiased ones, this bound allows us to fully characterize the Kirkwood-Dirac classical states as the eigenvectors of the two observables. We show furthermore that complete incompatibility implies several weaker notions of incompatibility, among which features a strong form of noncommutativity.

Dates and versions

hal-03911322 , version 1 (22-12-2022)

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Cite

Stephan De Bièvre. Relating incompatibility, noncommutativity, uncertainty and Kirkwood-Dirac nonclassicality. Journal of Mathematical Physics, 2023, 64 (2), pp.022202. ⟨10.1063/5.0110267⟩. ⟨hal-03911322⟩
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