Quantum coherence from Kirkwood-Dirac nonclassicality, some bounds, and operational interpretation

• URL: http://arxiv.org/abs/2309.09162v3
• Date: Thu, 23 May 2024 12:28:15 GMT
• Title: Quantum coherence from Kirkwood-Dirac nonclassicality, some bounds, and operational interpretation
• Authors: Agung Budiyono, Joel F. Sumbowo, Mohammad K. Agusta, Bagus E. B. Nurhandoko,
• Abstract summary: We develop a faithful quantifier of quantum coherence based on the KD nonclassicality. The KD-nonclassicality coherence captures simultaneously the nonreality and the negativity of the KD quasiprobability.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Just a few years after the inception of quantum mechanics, there has been a research program using the nonclassical values of some quasiprobability distributions to delineate the nonclassical aspects of quantum phenomena. In particular, in KD (Kirkwood-Dirac) quasiprobability distribution, the distinctive quantum mechanical feature of noncommutativity which underlies many nonclassical phenomena, manifests in the nonreal values and/or the negative values of the real part. Here, we develop a faithful quantifier of quantum coherence based on the KD nonclassicality which captures simultaneously the nonreality and the negativity of the KD quasiprobability. The KD-nonclassicality coherence thus defined, is upper bounded by the uncertainty of the outcomes of measurement described by a rank-1 orthogonal PVM (projection-valued measure) corresponding to the incoherent orthonormal basis which is quantified by the Tsallis $\frac{1}{2}$-entropy. Moreover, they are identical for pure states so that the KD-nonclassicallity coherence for pure state admits a simple closed expression in terms of measurement probabilities. We then use the Maassen-Uffink uncertainty relation for min-entropy and max-entropy to obtain a lower bound for the KD-nonclassicality coherence of a pure state in terms of optimal guessing probability in measurement described by a PVM noncommuting with the incoherent orthonormal basis. We also derive a trade-off relation for the KD-noncassicality coherences of a pure state relative to a pair of noncommuting orthonormal bases with a state-independent lower bound. Finally, we sketch a variational scheme for a direct estimation of the KD-nonclassicality coherence based on weak value measurement and thereby discuss its relation with quantum contextuality.

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