Intrinsic NDWU extension to measurements with more outcomes

Develop an intrinsic extension of the common-overlap No-Disturbance-without-Uncertainty principle to Bell scenarios in which both parties have measurements with more than two outcomes, beyond the necessary conditions obtained from binary coarse-grainings.

Background

The paper proves that the convex hull of behaviors satisfying the common-overlap No-Disturbance-without-Uncertainty criterion coincides with the finite-dimensional quantum set when one party has two binary measurements, including the simplest (2,2;2,2) Bell scenario and the one-sided generalization with arbitrary finite settings and outcomes for the other party.

For scenarios with more outcomes, the paper only derives necessary outer conditions by coarse-graining each measurement into two outcomes and applying the binary result. It does not provide an intrinsic formulation of the No-Disturbance-without-Uncertainty principle for the original multi-outcome measurements, nor establish whether such a formulation can characterize the corresponding quantum set.