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

• URL: http://arxiv.org/abs/2310.16471v1
• Date: Wed, 25 Oct 2023 08:52:00 GMT
• Title: Violation of the two-time Leggett-Garg inequalities for a harmonic oscillator
• Authors: Kosei Hatakeyama, Daisuke Miki, Masaki Tani, Yuuki Yamasaki, Satoshi Iso, Apriadi Salim Adam, Ar Rohim, Kazuhiro Yamamoto
• Abstract summary: We develop a new formula to compute the two-time quasi-probability distribution function. We discuss when the Leggett-Garg inequalities are violated in an intuitive manner.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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