Large violation of Leggett-Garg inequalities with coherent-state projectors for a harmonic oscillator and chiral scalar field

• URL: http://arxiv.org/abs/2401.10692v2
• Date: Mon, 29 Jan 2024 08:02:31 GMT
• Title: Large violation of Leggett-Garg inequalities with coherent-state projectors for a harmonic oscillator and chiral scalar field
• Authors: Tomoya Hirotani, Akira Matsumura, Yasusada Nambu, Kazuhiro Yamamoto
• Abstract summary: We investigate violations of Leggett-Garg inequalities (LGIs) for a harmonic oscillator and a (1+1)-dimensional chiral scalar field with coherent-state projectors. We find that the vacuum and thermal states violated the LGIs by evaluating the two-time quasi-probability distribution function. We also find a violation of the LGIs for the local mode of a quantum chiral scalar field by constructing a coherent-state projector.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 L\"uders 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.

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