Geometry of the quantum set on no-signaling faces

Abstract

Since Bell's theorem we know that quantum mechanics is incompatible with local hidden-variable models, the phenomenon known as quantum nonlocality. However, despite steady progress over the years, precise characterization of the set of quantum correlations remained elusive. There are correlations compatible with the no-signaling principle and still beyond what can be achieved within quantum theory, which has motivated the search for physical principles and computational methods to decide the quantum or postquantum behavior of correlations. Here, we identify a feature of Bell correlations that we call quantum voids: faces of the no-signaling set where all nonlocal correlations are postquantum. Considering the simplest possible Bell scenario, we give a full characterization of quantum voids, also understanding its connections to known principles and its potential use as a dimension witness. arXiv:1812.06057v2 [quant-ph]

Nonlocality distillation and quantum voids

“…Our results can be used to extend that. As shown in [35], some correlations of the 2D quantum voids do not violate Uffink's inequality (see Fig. 3).…”

“…, 8). Here, we follow the notation in [35], as shown in Table I. As will be described in more details below, we are interested here in nonlocality distillation.…”

“…Following [35], we represent a probability distribution p(ab|xy) as a vector (p 1 , p 2 , ..., p 16 ), where the ordering of probabilities is as shown in Table II. On considering the probabilities p 2 , p 3 , p 6 , p 7 , p 10 , p 11 , p 13 and p 16 as free variables, the remaining eight probabilities can be expressed in terms of the free variables by using no-signaling and normalization conditions.…”

Observers of quantum systems cannot agree to disagree

“…By ref. 22 , the boxes of Theorem 7 are either local or postquantum. But Theorem 6 implies they cannot be local.…”

“…We are grateful to Elie Wolfe for bringing ref. 22 to our attention, Alex Pozas-Kerstjens for help with the numerical search, Miguel Navascués for spotting a mistake in a previous version of the paper, Ronald de Wolf, Serge Fehr, Rena Henderson, Laura Mančinska, and Peter van Emde Boas. We acknowledge financial support from NYU Stern School of Business, NYU Shanghai, and J.P. Valles (A.B.…”