Detecting the nonlocality of many-body quantum states

Jordi Tura¹, Remigiusz Augusiak¹, Ana Belén Sainz¹, Tamás Vértesi², Maciej Lewenstein^1,3 and Antonio Acín^1,3

¹ICFO-Institut de Ciències Fotòniques, 08860 Castelldefels (Barcelona), Spain

²Institute for Nuclear Research, Hungarian Academy of Sciences, H-4001 Debrecen, P.O. Box 51, Hungary

³ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluís Companys 23, 08010 Barcelona, Spain

One of the most important steps in the understanding of quantum many-body systems is due to the intensive studies of their entanglement properties. Much less, however, is known about the role of quantum nonlocality in these systems. This is because standard manybody observables involve correlations among few particles, while there is no multipartite Bell inequality for this scenario. Here [1] we provide the first example of nonlocality detection in many-body systems using only two-body correlations. To this aim, we construct families of multipartite Bell inequalities that involve only second order correlations of local observables. We then provide examples of systems, relevant for nuclear and atomic physics, whose ground states violate our Bell inequalities for any number of constituents. Finally, we identify inequalities that can be tested by measuring collective spin components, opening the way to the experimental detection of many-body nonlocality, for instance with atomic ensembles.

[1] J. Tura et al, arXiv:1306.6860, accepted for publication in Science.