Leggett-Garg inequalities for multitime processe

We study some aspects of the Leggett-Garg inequalities by using the operator-state formalism for multitime processes. A new type of temporal quantum state, which we call process states, is introduced to investigate the Leggett-Garg inequalities and their violations. We find the sufficient conditions on process states for the Leggett-Garg inequalities to hold, in line with the no-signaling in time conditions. Based on these new conditions on process states, we find a new way of characterizing the environmental influences on the violation of Leggett-Garg inequalities through the structure of process states.Comment: 11 page