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Science China Physics Mechanics and Astronomy

Kirkwood-Dirac nonclassicality advantages on quantum steering

Bingke Zheng, Zhihua Guo, Huaixin Cao, Zhihao Ma, Zhihua Chen, Shao-Ming Fei

Published Sep 29, 2025• 2 citations
Publisher
DOI
10.1007/s11433-025-2785-2

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The Kirkwood-Dirac (KD) quasiprobability is a quantum analog expression of the phase-space probability in classical statistical mechanics, yet it can behave nonclassically by taking negative or nonreal values. The nonclassicality of the KD quasiprobability distribution has lately been shown to provide advantages in some quantum information tasks and shed light on a number of aspects of quantum physics. Characterization and quantification of KD nonclassicality are crucial both theoretically and experimentally. Most of the existing measures of KD nonclassicality concentrate merely on the negative or/and imaginary part(s) of the KD distribution. Yet it is not clear whether these measures can account for all nonclassicality in the distribution. In this paper, we suggest a KD nonclassicality measure based on the two quantum modification terms in the quasiprobability distribution. The present paper is mainly motivated by the following two considerations: First, the two quantum modification terms are actually the sources of the negative and imaginary parts of the KD quasiprobability respectively. Secondly, these quantum modification terms deviate the KD quasiprobability from the classical joint probability distribution function of two successive projective measurements (termed as the Wigner formula), which can be obtained from the multiplication principle in classical probability theory. Our measure refines the quantification of KD nonclassicality in the sense that even for real and nonnegative KD distribution, its quantum modification terms can still exist, resulting in a nonvanishing KD nonclassicality. As an illustration, we analyze the KD nonclassicality of the positive KD distribution in the postselected metrology scheme [S. Das, S. Modak, and M. N. Bera, Phys. Rev. A 107, 042413 (2023)], which provides interpretation on the source of quantum advantages. We also give an upper bound on the KD nonclassicality measure and offer an easily verifiable sufficient condition for nonvanishing KD nonclassicality.