Quantum correlations on the no-signaling boundary: self-testing and more

In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play fundamental role. Even though it is long-known that the set of allowed theory lies strictly Bell-local and no-signaling set, many questions concerning geometry remain unanswered. Here, we revisit problem when boundary coincides with simplest scenario. particular, for each Class these common boundaries containing $k$ zero probabilities, provide $(5-k)$-parameter family strategies realizing (extremal) correlations. We further prove self-testing possible all nontrivial Classes beyond known examples Hardy-type correlations, numerical evidence supporting robustness results. Candidates one-parameter families from some are identified. As byproduct our investigation, if qubit leading to an extremal nonlocal correlation local-unitarily equivalent, statement provably follows. Interestingly, found on non-exposed. An analogous characterization $\mathcal{M}$ arising finite-dimensional maximally entangled states also provided. En route establishing this last result, show scenario attainable as convex combinations those achievable using pair projective measurements. turn, obtain maximal Clauser-Horne-Shimony-Holt inequality violation any two-qudit state no-go theorem regarding such states.