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Journal Articles Physical Review Letters Year : 2021

Complete Incompatibility, Support Uncertainty, and Kirkwood-Dirac Nonclassicality

Abstract

Given two orthonormal bases in a d-dimensional Hilbert space, one associates to each state its Kirkwood-Dirac (KD) quasi-probability distribution. KD-nonclassical states - for which the KD-distribution takes on negative and/or nonreal values - have been shown to provide a quantum advantage in quantum metrology and information, raising the question of their identification. Under suitable conditions of incompatibility between the two bases, we provide sharp lower bounds on the support uncertainty of states that guarantee their KD-nonclassicality. In particular, when the bases are completely incompatible, a notion we introduce, states whose support uncertainty is not equal to its minimal value d+1 are necessarily KD-nonclassical. The implications of these general results for various commonly used bases, including the mutually unbiased ones, and their perturbations, are detailed.

Dates and versions

hal-03464950 , version 1 (03-12-2021)

Identifiers

Cite

Stephan de Bièvre. Complete Incompatibility, Support Uncertainty, and Kirkwood-Dirac Nonclassicality. Physical Review Letters, 2021, ⟨10.1103/PhysRevLett.127.190404⟩. ⟨hal-03464950⟩
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