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arXiv · 2401.10692

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

Tomoya Hirotani·Akira Matsumura·Yasusada Nambu·Kazuhiro Yamamoto
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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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Tomoya Hirotani, Akira Matsumura, Yasusada Nambu, Kazuhiro Yamamoto. 2024-01-19. Large violation of Leggett-Garg inequalities with coherent-state projectors for a harmonic oscillator and chiral scalar field. https://arxiv.org/abs/2401.10692

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