TY - JOUR

T1 - Nonlocality in many-body quantum systems detected with two-body correlators

AU - Tura, J.

AU - Augusiak, R.

AU - Sainz, A. B.

AU - Lücke, B.

AU - Klempt, C.

AU - Lewenstein, M.

AU - Acín, A.

N1 - Funding information: We thank Joe Eberly, Markus Oberthaler, Julia Stasi?ska, and Tamás Vértesi for enlightening discussions. This work was supported by Spanish MINECO projects FOQUS and a AP2009-1174 FPU Ph.D. grant, the EU IP SIQS, ERC AdG OSYRIS and CoG QITBOX, the Generalitat de Catalunya and the John Templeton Foundation. C. K. and B. L. acknowledge support from the Centre for Quantum Engineering and Space-Time Research (QUEST) ( EXC 201 ) and from the Deutsche Forschungsgemeinschaft ( Research Training Group 1729 ).

PY - 2015/7/30

Y1 - 2015/7/30

N2 - Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Tura et al., Science 344 (2014) 1256]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states-ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.

AB - Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Tura et al., Science 344 (2014) 1256]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states-ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.

KW - Bell inequalities

KW - Bell nonlocality

KW - Many body systems

KW - Quantum nonlocality

UR - http://www.scopus.com/inward/record.url?scp=84940054364&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2015.07.021

DO - 10.1016/j.aop.2015.07.021

M3 - Article

AN - SCOPUS:84940054364

VL - 362

SP - 370

EP - 423

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -