  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.
