Unrestricted optimum and dimensionality of the I3322 inequality

Determine the unrestricted quantum optimum of the two-party I3322 Bell inequality and establish whether attaining that optimum requires an infinite-dimensional quantum system.

Background

The paper studies the two-party I3322 inequality, whose violation exceeds the value achievable by the displayed qubit strategy when higher-dimensional constructions are allowed. Numerical evidence suggests that the optimum may be approached only as the local Hilbert-space dimension increases without bound. The paper presents this as a conjectural issue rather than resolving the exact unrestricted optimum or proving the necessity of infinite dimension.

References

the unrestricted optimum and the need for infinite dimension were conjectured on numerical evidence

— Trade-offs and experimental feasibility of nonlocal polygamy with two-outcome Bell inequalities  (2609.24835 - Batle et al., 21 Sep 2026) in Section “I3322 polygamy”