Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Distinguishing three-body from two-body nonseparability by a Bell-type inequality

George Svetlichny

Published May 15, 1987• 668 citations
Publisher

Abstract

We derive an inequality, violated by quantum mechanics, that in a three-body system can detect three-body correlations that cannot be reduced to mixtures of two-body ones related locally to the third body.
DOI
10.1103/physrevd.35.3066

Related papers

Bell-Type Inequalities to Detect True n -Body Nonseparability

Daniel Collins, Nicolas Gisin, Sandu Popescu +2 more

We analyze the structure of correlations among more than two quantum systems. We introduce a classification of correlations based on the concept of nonseparability, which is different a priori from the concept of entanglement. Generalizing a result of Svetlichny [Phys. Rev. D 35, 3066 (1987)] on three-particle correlations, we find an inequality for n-particle correlations that holds under the most general separability condition and that is violated by some quantum-mechanical states.

arXiv:quant-ph/0201058•Physical Review Letters•Apr 12, 2002•298 citations

Information and quantum nonseparability

Berthold W. Schumacher

An information-theoretic inequality analogous to the well-known result of Bell [Physics 1, 195 (1964)] is formulated using the concept of information distance. This inequality, like Bell's, is true for all local-hidden-variable theories, but not for quantum mechanics. The metric space structure of this new inequality suggests a reformulation of familiar Bell inequalities in terms of a ``covariance distance.'' Quantum nonseparability can be demonstrated through violations of these inequalities even in cases where the correlation between two systems is extremely weak. The connection between nonseparability and complementarity is also briefly discussed in this paper.

Physical Review A•Dec 1, 1991•43 citations

Detecting nonlocality in many-body quantum states

Jordi Tura, Remigiusz Augusiak, Ana Belén Sainz +3 more

Intensive studies of entanglement properties have proven essential for our understanding of quantum many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems because the available multipartite Bell inequalities involve correlations among many particles, which are difficult to access experimentally. We constructed multipartite Bell inequalities that involve only two-body correlations and show how they reveal the nonlocality in many-body systems relevant for nuclear and atomic physics. Our inequalities are violated by any number of parties and can be tested by measuring total spin components, opening the way to the experimental detection of many-body nonlocality, for instance with atomic ensembles.

arXiv:1306.6860•Science•Jun 12, 2014•209 citations

Entanglement and Nonlocality in Many-Body Systems: a primer

Jordi Tura, Ana Belén Sainz, Grass, T. +3 more

Current understanding of correlations and quantum phase transitions in many-body systems has significantly improved thanks to the recent intensive studies of their entanglement properties. In contrast, much less is known about the role of quantum non-locality in these systems. On the one hand, standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. On the other hand, most of the available multipartite Bell inequalities involve correlations among many particles. Such correlations are notoriously hard to access theoretically, and even harder experimentally. Typically, there is no Bell inequality for many-body systems built only from low-order correlation functions. Recently, however, it has been shown in [J. Tura et al., Science 344, 1256 (2014)] that multipartite Bell inequalities constructed only from two-body correlation functions are strong enough to reveal non-locality in some many-body states, in particular those relevant for nuclear and atomic physics. The purpose of this lecture is to provide an overview of the problem of quantum correlations in many-body systems - from entanglement to nonlocality - and the methods for their characterization.

arXiv:1501.02733•Jan 12, 2015•11 citations

Strong violations of Bell-type inequalities for Werner-like states

Christoph F. Wildfeuer, Jonathan P. Dowling

We investigate the violation of Bell-type inequalities for two-qubit Werner-like states parametrized by the positive parameter $0\ensuremath{\leqslant}p\ensuremath{\leqslant}1$. We use an unbalanced homodyne detection scheme to obtain the quantum mechanical probabilities. A violation of the Bell-Wigner and Janssens inequalities is obtained for a large range of the parameter $p$. The range given by these inequalities is greater than the one given by the Clauser-Horne inequality. The range in which a violation is attained actually coincides with the range where the Werner-like states are known to be nonseparable, i.e., for $p>1∕3$. However, the improvement over the Clauser-Horne inequality is achieved at the price of restricting the class of possible local hidden variable theories.

arXiv:0708.1973•Physical Review A•Sep 18, 2008•8 citations

Unconditional Quantum Correlations do not Violate Bell’s Inequality

Andrei Yu. Khrennikov

arXiv:1503.08016•Foundations of Physics•Jul 3, 2015•2 citations
An information-theoretic inequality analogous to the well-known result of Bell [Physics 1, 195 (1964)] is formulated using the concept of information distance. This inequality, like Bell's, is true for all local-hidden-variable theories, but not for quantum mechanics. The metric space structure of this new inequality suggests a reformulation of familiar Bell inequalities in terms of a ``covariance distance.'' Quantum nonseparability can be demonstrated through violations of these inequalities even in cases where the correlation between two systems is extremely weak. The connection between nonseparability and complementarity is also briefly discussed in this paper.
Intensive studies of entanglement properties have proven essential for our understanding of quantum many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems because the available multipartite Bell inequalities involve correlations among many particles, which are difficult to access experimentally. We constructed multipartite Bell inequalities that involve only two-body correlations and show how they reveal the nonlocality in many-body systems relevant for nuclear and atomic physics. Our inequalities are violated by any number of parties and can be tested by measuring total spin components, opening the way to the experimental detection of many-body nonlocality, for instance with atomic ensembles.
Current understanding of correlations and quantum phase transitions in many-body systems has significantly improved thanks to the recent intensive studies of their entanglement properties. In contrast, much less is known about the role of quantum non-locality in these systems. On the one hand, standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. On the other hand, most of the available multipartite Bell inequalities involve correlations among many particles. Such correlations are notoriously hard to access theoretically, and even harder experimentally. Typically, there is no Bell inequality for many-body systems built only from low-order correlation functions. Recently, however, it has been shown in [J. Tura et al., Science 344, 1256 (2014)] that multipartite Bell inequalities constructed only from two-body correlation functions are strong enough to reveal non-locality in some many-body states, in particular those relevant for nuclear and atomic physics. The purpose of this lecture is to provide an overview of the problem of quantum correlations in many-body systems - from entanglement to nonlocality - and the methods for their characterization.
We investigate the violation of Bell-type inequalities for two-qubit Werner-like states parametrized by the positive parameter $0\ensuremath{\leqslant}p\ensuremath{\leqslant}1$. We use an unbalanced homodyne detection scheme to obtain the quantum mechanical probabilities. A violation of the Bell-Wigner and Janssens inequalities is obtained for a large range of the parameter ppp. The range given by these inequalities is greater than the one given by the Clauser-Horne inequality. The range in which a violation is attained actually coincides with the range where the Werner-like states are known to be nonseparable, i.e., for p>1∕3p>1∕3p>1∕3. However, the improvement over the Clauser-Horne inequality is achieved at the price of restricting the class of possible local hidden variable theories.