Objectivity, nonlocality, and the Bell inequalities

Peter Rastall

Albert Aloy López

Nonlocality detection in multipartite quantum systems is of great interest. The most popular tool to detect nonlocality in quantum systems are Bell inequalities. Most of the provided constructions of multipartite Bell inequalities involve correlations between all parties which quickly becomes computationally intractable and hard to test experimentally in many-body quantum systems. Recently, J. Tura and collaborators have shown in [Science 344.6189 (2014): 1256-1258] that detection of nonlocality in multipartite systems is possible with Bell inequalities involving only one- and two- body correlation functions. However, it is uncertain how efficient these new inequalities are. One of the objectives of the present work is to address this question by numerical means. The other objective is to show that these inequalities can also serve as as device independent witnesses of different forms of entanglement such as genuine multipartite entanglement.

Justo Pastor Lambare

Despite their Nobel Prize-winning empirical implementation, the Bell inequality interpretation remains controversial. An objective analysis of Bell's work on nonlocality shows that Bell's rationale calls for reconsidering a widespread argument on quantum nonlocality, yielding a precise formulation free from the usual obscurities that lead to misleading controversies. By dismissing unnecessary metaphysical tenets, it is possible to probe the core of the problem and determine under what rational assumptions locality or nonlocality become feasible alternatives clarifying their relation to the Bell inequality. The approach renders a more balanced perspective over a long-standing polarized interpretative debate.

Christoph Spengler, Marcus Huber, Beatrix C. Hiesmayr

We compare entanglement with quantum nonlocality employing a geometric structure of the state space of bipartite qudits. Central object is a regular simplex spanned by generalized Bell states. The Collins-Gisin-Linden-Massar-Popescu-Bell inequality is used to reveal states of this set that cannot be described by local-realistic theories. Optimal measurement settings necessary to ascertain nonlocality are determined by means of a recently proposed parameterization of the unitary group U(d) combined with robust numerical methods. The main results of this paper are descriptive geometric illustrations of the state space that emphasize the difference between entanglement and quantum nonlocality. Namely, it is found that the shape of the boundaries of separability and Bell inequality violation are essentially different. Moreover, it is shown that also for mixtures of states sharing the same amount of entanglement, Bell inequality violations and entanglement measures are non-monotonically related.

Marian Kupczyński