Leggett-Garg inequalities for multitime processes

We study some aspects of the Leggett-Garg inequalities by using the operator-state formalism for multitime processes. The process tensor in its Choi-state form, which we call process state, is employed to investigate the Leggett-Garg inequalities and their violations. We find the sufficient conditions on process states for the Leggett-Garg inequalities to hold, based on which we find a new way of characterizing the influences on the violation of Leggett-Garg inequalities through the structure of process states.