Entanglement, non-Markovianity, and causal non-separability

Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means of non-Markovian dynamics with a measurement on additional degrees of freedom. Explicitly, we provide a constructive scheme to implement arbitrary acausal processes. Furthermore, we give necessary and sufficient conditions for open system dynamics with measurement to yield processes that respect causality locally, and find that tripartite entanglement and nonlocal unitary transformations are crucial requirements for the simulation of causally indefinite processes. These results show a direct connection between three counter-intuitive concepts: non-Markovianity, entanglement, and causal indefiniteness.