We investigate the violation of the Leggett-Garg inequalities for a quantum field, focusing on the two-time quasiprobability distribution function of the dichotomic variable with a coarse-grained scalar field. The Leggett-Garg inequalities are violated depending on the quantum state of the field and the size of coarse graining. We demonstrate that the violation of the Leggett-Garg inequalities appears even for the vacuum state and the squeezed state by properly constructing the dichotomic variable and the projection operator.
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Tani et al. (2024) studied this question.
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