GHZ optimality conjecture for correlated 3×2×2 Bell proofs

A $3\times2\times2$ proof is a Bell-nonlocality proof with three settings for one party and two settings and two outcomes for each of the other parties. A setting distribution may be correlated when the parties' measurement settings are sampled jointly. GHZ denotes the Greenberger–Horne–Zeilinger proof.

GHZ optimality conjecture. Among all $3\times2\times2$ proofs, and allowing correlated setting distributions, GHZ is best.

This conjecture proposes GHZ as the strongest proof in this three-party binary-outcome class under correlated setting distributions. It is based on numerical analysis in the paper and is not proved there, so it remains open.