A coherence monotone from Kirkwood-Dirac nonclassicality with respect to mutually unbiased bases
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918051617701888 |
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| author | Liu, Yan Guo, Zhihua Ma, Zhihao Fei, Shao-Ming |
| author_facet | Liu, Yan Guo, Zhihua Ma, Zhihao Fei, Shao-Ming |
| contents | The Kirkwood-Dirac distribution, serving as an informationally complete representation of a quantum state, has recently garnered increasing attention. We investigate the Kirkwood-Dirac classicality with respect to mutually unbiased bases. For prime dimensional Hilbert spaces, {we demonstrate that a quantum state exhibits Kirkwood-Dirac classicality for two distinct sets of mutually unbiased bases $(A,B)$ and $(A,B')$ if and only if it is incoherent with respect to $A$}. We subsequently introduce a coherence monotone based on Kirkwood-Dirac nonclassicality with respect to mutually unbiased bases. Additionally, we establish that this coherence monotone can be expressed through weak values, suggesting that quantum coherence can be utilized to detect anomalous weak values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A coherence monotone from Kirkwood-Dirac nonclassicality with respect to mutually unbiased bases Liu, Yan Guo, Zhihua Ma, Zhihao Fei, Shao-Ming Quantum Physics The Kirkwood-Dirac distribution, serving as an informationally complete representation of a quantum state, has recently garnered increasing attention. We investigate the Kirkwood-Dirac classicality with respect to mutually unbiased bases. For prime dimensional Hilbert spaces, {we demonstrate that a quantum state exhibits Kirkwood-Dirac classicality for two distinct sets of mutually unbiased bases $(A,B)$ and $(A,B')$ if and only if it is incoherent with respect to $A$}. We subsequently introduce a coherence monotone based on Kirkwood-Dirac nonclassicality with respect to mutually unbiased bases. Additionally, we establish that this coherence monotone can be expressed through weak values, suggesting that quantum coherence can be utilized to detect anomalous weak values. |
| title | A coherence monotone from Kirkwood-Dirac nonclassicality with respect to mutually unbiased bases |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.11666 |