Details
| Original language | English |
|---|---|
| Pages (from-to) | 370-423 |
| Number of pages | 54 |
| Journal | Annals of Physics |
| Volume | 362 |
| Publication status | Published - 30 Jul 2015 |
Abstract
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.
Keywords
- Bell inequalities, Bell nonlocality, Many body systems, Quantum nonlocality
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Annals of Physics, Vol. 362, 30.07.2015, p. 370-423.
Research output: Contribution to journal › Article › Research › peer review
}
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 -