Admissible Causal Structures and Correlations

Abstract

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.

arXiv comment11 pages, 6 figures, extended preliminaries, details on numerical calculations, reference to source code, numerical test increased to six nodes. Comments welcome!

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Cited by in corpus (5)

• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• The Möbius game and other Bell tests for relativity
• Consistent circuits for indefinite causal order
• No quantum advantage for violating fixed-order inequalities?
• Flow of dynamical causal structures with an application to correlations