  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.
