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Adán Cabello

Universidad de Sevilla, Spain, adan@us.es

What is the relation between AVN, PT, and FN?

contextuality vs causality

All-vs-nothing (AVN) nonlocality, pseudo-telepathy (PT), and full nonlocality (FN) are three extreme forms of Bell nonlocality. A matrix of correlations produces AVN nonlocality if it yields a list L of predictions with certainty about a result of an experiment without in any way disturbing it such that, using Einstein-Podolsky-Rosen criterion of element of reality, all but one of the predictions in L lead to a conclusion which is in contradiction with the remaining prediction in L. PT allows two (or more) spacelike separated players to always win a game which is impossible to win classically unless they communicate, hence suggesting a seemingly telepathic connection between them. A matrix of correlations has FN if the maximum local weight of all its possible decompositions in terms of local and nonsignaling correlations is zero. Quantum mechanics allows for AVN, PT, and FN. It is known that neither bipartite AVN nor PT can be achieved with qubit-qubit entanglement. It is known that PT cannot be achieved using only two-outcome measurements or if one of the players only has two measurement settings. Similarly, it is known that bipartite FN cannot be achieved in the simplest Bell scenario. In addition, the simplest known examples of bipartite AVN, PT, and FN are based on the same matrix of correlations. However, an open question is: What is the relation between AVN, PT, and FN? Here, we will address this question.