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Proposed principles remove many of them, but none so far gives exactly the quantum set.","posed_since":"1994","precise":"Find a physical or information-theoretic principle $P$, stated without Hilbert space, such that the set of bipartite and multipartite behaviors $p(ab...\\mid xy...)$ satisfying $P$, closed under wirings and composition, equals the quantum set $Q$ or its closure. Known principles (non-trivial communication complexity, information causality, macroscopic locality, local orthogonality) are either satisfied by the almost-quantum set, which strictly contains $Q$, or not known to exclude it.","problem_ref":null,"references":"","settled_by":"A principle with proofs that Q satisfies it and every non-quantum behavior violates it.","status_note":"Gallego et al. 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