Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems
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| Format: | Preprint |
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2023
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| _version_ | 1866910389404434432 |
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| author | Umekawa, Shun Lee, Jaeha Hatano, Naomichi |
| author_facet | Umekawa, Shun Lee, Jaeha Hatano, Naomichi |
| contents | We investigate features of the quasi-joint-probability distribution for finite-state quantum systems, especially the two-state and three-state quantum systems, comparing different types of quasi-joint-probability distributions based on the general framework of quasi-classicalization. We show from two perspectives that the Kirkwood-Dirac distribution is the quasi-joint-probability distribution that behaves nicely for the finite-state quantum systems. One is the similarity to the genuine probability and the other is the information that we can obtain from the quasi-probability. By introducing the concept of the possible values of observables, we show for the finite-state quantum systems that the Kirkwood-Dirac distribution behaves more similarly to the genuine probability distribution in contrast to most of the other quasi-probabilities including the Wigner function. We also prove that the states of the two-state and three-state quantum systems can be completely distinguished by the Kirkwood-Dirac distribution of only two directions of the spin and point out for the two-state system that the imaginary part of the quasi-probability is essential for the distinguishability of the state. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_06836 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems Umekawa, Shun Lee, Jaeha Hatano, Naomichi Quantum Physics Mathematical Physics We investigate features of the quasi-joint-probability distribution for finite-state quantum systems, especially the two-state and three-state quantum systems, comparing different types of quasi-joint-probability distributions based on the general framework of quasi-classicalization. We show from two perspectives that the Kirkwood-Dirac distribution is the quasi-joint-probability distribution that behaves nicely for the finite-state quantum systems. One is the similarity to the genuine probability and the other is the information that we can obtain from the quasi-probability. By introducing the concept of the possible values of observables, we show for the finite-state quantum systems that the Kirkwood-Dirac distribution behaves more similarly to the genuine probability distribution in contrast to most of the other quasi-probabilities including the Wigner function. We also prove that the states of the two-state and three-state quantum systems can be completely distinguished by the Kirkwood-Dirac distribution of only two directions of the spin and point out for the two-state system that the imaginary part of the quasi-probability is essential for the distinguishability of the state. |
| title | Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2309.06836 |