Figure 3.

Schematic representation of the collisional dynamics in the Markovian case. In panel (a), the system interacts with the first ancilla $E_1$ through the unitary map ${\mathcal{U}}_{S{E}_1}$. In panel (b), after the interaction has taken place, the ancilla $E_1$ is traced away, leaving us with the state of the system after the interaction ${\widehat{\rho }}_S\left(\delta t\right)$. Then in panel (c), the system interacts with the second ancilla $E_2$ through the unitary map ${\mathcal{U}}_{S{E}_2}$. Finally, in panel (d), the ancilla $E_2$ is traced away, leaving us with the state ${\widehat{\rho }}_S\left(2\delta t\right)$. Repeating these two steps, interaction and tracing, for all the ancillas, gives rise to the open system dynamics of S.