Which principle singles out exactly the quantum correlations?
In plain words
No-signalling allows superstrong correlations, such as the Popescu-Rohrlich box, that quantum mechanics forbids. Proposed principles remove many of them, but none so far gives exactly the quantum set.
Precise statement
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.
What would settle it
A principle with proofs that Q satisfies it and every non-quantum behavior violates it.
Status in the literature
Gallego et al. (2011) showed that bipartite principles alone cannot recover multipartite quantum correlations.
Related problems
- More general than Do almost-quantum correlations satisfy information causality?
- More general than Does information causality exclude every post-quantum box with two binary inputs?