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arXiv · 2310.16471

Violation of the two-time Leggett-Garg inequalities for a harmonic oscillator

Kosei Hatakeyama·Daisuke Miki·Masaki Tani·Yuuki Yamasaki·Satoshi Iso·Apriadi Salim Adam·Ar Rohim·Kazuhiro Yamamoto
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Abstract

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.

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Kosei Hatakeyama, Daisuke Miki, Masaki Tani, Yuuki Yamasaki, Satoshi Iso, Apriadi Salim Adam, Ar Rohim, Kazuhiro Yamamoto. 2023-10-25. Violation of the two-time Leggett-Garg inequalities for a harmonic oscillator. https://doi.org/10.1103/physreva.110.012223

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