Quantum coherence from Kirkwood-Dirac nonclassicality, some bounds, and operational interpretation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909208482414592 |
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| author | Budiyono, Agung Sumbowo, Joel F. Agusta, Mohammad K. Nurhandoko, Bagus E. B. |
| author_facet | Budiyono, Agung Sumbowo, Joel F. Agusta, Mohammad K. Nurhandoko, Bagus E. B. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09162 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum coherence from Kirkwood-Dirac nonclassicality, some bounds, and operational interpretation Budiyono, Agung Sumbowo, Joel F. Agusta, Mohammad K. Nurhandoko, Bagus E. B. Quantum Physics 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. |
| title | Quantum coherence from Kirkwood-Dirac nonclassicality, some bounds, and operational interpretation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2309.09162 |