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Admissible Causal Structures and Correlations
It is well-known that if one assumes quantum theory to hold locally, then
processes with indefinite causal order and cyclic causal structures become
feasible. Here, we study qualitative limitations on causal structures and
correlations imposed by local quantum theory. For one, we find a necessary
graph theoretic criterion--the "siblings-on-cycles" property--for a causal
structure to be admissible: Only such causal structures admit a realization
consistent with local quantum theory. We conjecture that this property is
moreover sufficient. This conjecture is motivated by an explicit construction
of quantum causal models, and supported by numerical calculations. We show that
these causal models, in a restricted setting, are indeed consistent. For
another, we identify two sets of causal structures that, in the
classical-deterministic case, give rise to causal and non-causal correlations
respectively.Comment: 11 pages, 6 figures, extended preliminaries, details on numerical
calculations, reference to source code, numerical test increased to six
nodes. Comments welcome