QI In the literature: partially resolved

Does information causality exclude every post-quantum box with two binary inputs?

In plain words

In the simplest Bell test each side picks one of two measurements with two outcomes. A 2026 result shows a strengthened information-causality principle reproduces the quantum boundary when each local outcome is equally likely, but whether it excludes every non-quantum box, including ones with biased local outcomes, is open.

Precise statement

In the $(2,2,2)$ Bell scenario, generalized information causality implies the Tsirelson-Landau-Masanes criterion $\left|\operatorname{asin} C_{00}+\operatorname{asin} C_{01}+\operatorname{asin} C_{10}-\operatorname{asin} C_{11}\right|\le\pi$ on the correlators $C_{xy}=\langle a_x b_y\rangle$, which characterizes $Q$ when $\langle a_x\rangle=\langle b_y\rangle=0$, and is strictly stronger than macroscopic locality (Gachechiladze and Miklin, arXiv:2609.10508). Determine whether it excludes every non-quantum behavior with nonzero marginals.

What would settle it

A proof that generalized information causality implies membership in Q for all (2,2,2) behaviors, or an explicit non-quantum behavior that satisfies it.

Status in the literature

Unverified note

The TLM criterion for unbiased marginals was derived from generalized information causality in September 2026 (arXiv:2609.10508); the case of nonzero marginals is not addressed there.