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Cyclic quantum causal models and violations of causal inequalities

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I will present an extension of the recent theory of quantum causal models to cyclic causal structures. This offers a novel causal perspective on processes beyond those corresponding to standard circuits, such as processes with dynamical causal order and causally nonseparable processes, including processes violating causal inequalities. As an application, I will use the algebraic structure of process operators that is induced by the causal structure to prove that all unitarily extendible bipartite processes are causally separable, i.e., their unitary extensions are variations of the quantum SWITCH. Remarkably, the latter implies that all unitarily extendible tripartite quantum processes have realizations on time-delocalized systems within standard quantum mechanics. This includes, in particular, classical processes violating causal inequalities, which admit simple implementations! I will explain what the violation of causal inequalities implies for the variables of interest in these implementations. The answer is given again by the theory of cyclic causal models.
Based on joint works with Jonathan Barrett, Cyril Branciard, Robin Lorenz, and Julian Wechs.