Violation of the two-time Leggett-Garg inequalities for a harmonic oscillator
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916876217483264 |
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| author | Hatakeyama, Kosei Miki, Daisuke Tani, Masaki Yamasaki, Yuuki Iso, Satoshi Adam, Apriadi Salim Rohim, Ar Yamamoto, Kazuhiro |
| author_facet | Hatakeyama, Kosei Miki, Daisuke Tani, Masaki Yamasaki, Yuuki Iso, Satoshi Adam, Apriadi Salim Rohim, Ar Yamamoto, Kazuhiro |
| contents | We investigate the violation of the Leggett-Garg inequalities for a harmonic oscillator in various quantum states. We focus on the two-time quasi-probability distribution function with a dichotomic variable constructed with the position operator of a harmonic oscillator. First, we developed a new formula to compute the two-time quasi-probability distribution function, whose validity is demonstrated in comparison with the formula developed in the recent paper by Mawby and Halliwell[Phys.Rev.A, 107 032216 (2023)]. Second, we demonstrated the variety of the violation of the two-time Leggett-Garg inequalities assuming various quantum states of a harmonic oscillator including the squeezed coherent state and the thermal squeezed coherent state. Third, we demonstrated that a certain type of extension of the dichotomic variable and the corresponding projection operator can boost violation of the Leggett-Garg inequalities for the ground state and the squeezed state. We also discuss when the Leggett-Garg inequalities are violated in an intuitive manner. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_16471 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Violation of the two-time Leggett-Garg inequalities for a harmonic oscillator Hatakeyama, Kosei Miki, Daisuke Tani, Masaki Yamasaki, Yuuki Iso, Satoshi Adam, Apriadi Salim Rohim, Ar Yamamoto, Kazuhiro Quantum Physics We investigate the violation of the Leggett-Garg inequalities for a harmonic oscillator in various quantum states. We focus on the two-time quasi-probability distribution function with a dichotomic variable constructed with the position operator of a harmonic oscillator. First, we developed a new formula to compute the two-time quasi-probability distribution function, whose validity is demonstrated in comparison with the formula developed in the recent paper by Mawby and Halliwell[Phys.Rev.A, 107 032216 (2023)]. Second, we demonstrated the variety of the violation of the two-time Leggett-Garg inequalities assuming various quantum states of a harmonic oscillator including the squeezed coherent state and the thermal squeezed coherent state. Third, we demonstrated that a certain type of extension of the dichotomic variable and the corresponding projection operator can boost violation of the Leggett-Garg inequalities for the ground state and the squeezed state. We also discuss when the Leggett-Garg inequalities are violated in an intuitive manner. |
| title | Violation of the two-time Leggett-Garg inequalities for a harmonic oscillator |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2310.16471 |