Do almost-quantum correlations satisfy information causality?
In plain words
The almost-quantum set is a slightly larger family than the quantum correlations that obeys nearly every principle proposed so far. If it also obeys information causality, that principle cannot single out quantum theory.
Precise statement
Determine whether every behavior in the almost-quantum set (level 1+AB of the Navascues-Pironio-Acin hierarchy, Navascues et al., Nature Communications 2015) satisfies information causality, in its original form and its generalized correlated-input form, for any number of copies and any wiring. An answer is a proof or an explicit almost-quantum box with a violating protocol.
What would settle it
A proof that the almost-quantum set obeys information causality, or an almost-quantum box with an information-causality-violating protocol.
Status in the literature
Unverified note
Stated as unresolved in arXiv:2609.10508 (September 2026).
Related problems
- Special case of Which principle singles out exactly the quantum correlations?