Effect of memory on the violation of Leggett-Garg inequality

The Leggett-Garg inequalities impose restrictions on the values taken by some combinations of the two-time correlation functions of observables in order to be explainable by a noninvasive-realist classical model. While in the unitary dynamics, it is straightforward to compute these correlation functions, open system effects bring in subtleties. Specifically, for non-Markovian dynamics, which involves setting up of system-bath correlations, the Leggett-Garg measurements disrupt these correlations, making a full system-bath Hamiltonian approach natural. However, here we point out that the problem can also be dealt with from a reduced dynamics perspective. The key point is that the noise superoperator acting on the system must be suitably updated after measurement interventions. Also considered is the effect of Markovian versus non-Markovian behavior as well as classically non-Markovian processes on the violation of Leggett-Garg inequalities.