Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
Phys. Rev. A 113, 032434 – Published 17 March, 2026
DOI: https://doi.org/10.1103/lkcb-nqqb
Abstract
The Kirkwood-Dirac (KD) distribution has recently emerged as a powerful quasiprobability framework with wide-ranging applications in quantum information processing tasks. In this work, we introduce an experimentally motivated criterion for detecting nonclassical signatures of the KD distribution using its statistical moments and demonstrate its effectiveness through explicit examples. We further show that this approach extends naturally to identify other quantum resources, such as quantum coherence and nonclassical extractable work, that are intrinsically connected to the KD distribution. Finally, we propose a methodology to realize these moments using a shadow tomography technique. Our criteria involve the evaluation of simple functionals, making it well suited for efficient experimental implementation.
