Large violation of Leggett-Garg inequalities with coherent-state projectors for a harmonic oscillator and chiral scalar field
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910309743067136 |
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| author | Hirotani, Tomoya Matsumura, Akira Nambu, Yasusada Yamamoto, Kazuhiro |
| author_facet | Hirotani, Tomoya Matsumura, Akira Nambu, Yasusada Yamamoto, Kazuhiro |
| contents | We investigate violations of Leggett-Garg inequalities (LGIs) for a harmonic oscillator and a (1+1)-dimensional chiral scalar field with coherent-state projectors, which is equivalent to a heterodyne-type measurement scheme. For the harmonic oscillator, we found that the vacuum and thermal states violated the LGIs by evaluating the two-time quasi-probability distribution function. In particular, we demonstrate that the value of the two-time quasi-probability reaches -0.123 for a squeezed coherent-state projector, which is equivalent to 98% of the Lüders bound corresponding to the maximal violation of the LGIs. We also find a violation of the LGIs for the local mode of a quantum chiral scalar field by constructing a coherent-state projector similar to the harmonic oscillator case. In contrast to the harmonic oscillator, the periodicity in the time direction of the quasi-probability disappears, which is related to the existence of quantum entanglement between the local mode and its complementary degrees of freedom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large violation of Leggett-Garg inequalities with coherent-state projectors for a harmonic oscillator and chiral scalar field Hirotani, Tomoya Matsumura, Akira Nambu, Yasusada Yamamoto, Kazuhiro Quantum Physics We investigate violations of Leggett-Garg inequalities (LGIs) for a harmonic oscillator and a (1+1)-dimensional chiral scalar field with coherent-state projectors, which is equivalent to a heterodyne-type measurement scheme. For the harmonic oscillator, we found that the vacuum and thermal states violated the LGIs by evaluating the two-time quasi-probability distribution function. In particular, we demonstrate that the value of the two-time quasi-probability reaches -0.123 for a squeezed coherent-state projector, which is equivalent to 98% of the Lüders bound corresponding to the maximal violation of the LGIs. We also find a violation of the LGIs for the local mode of a quantum chiral scalar field by constructing a coherent-state projector similar to the harmonic oscillator case. In contrast to the harmonic oscillator, the periodicity in the time direction of the quasi-probability disappears, which is related to the existence of quantum entanglement between the local mode and its complementary degrees of freedom. |
| title | Large violation of Leggett-Garg inequalities with coherent-state projectors for a harmonic oscillator and chiral scalar field |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.10692 |