All-multipartite Bell-correlation inequalities for two dichotomic observables per site

By Reinhard F. Werner, Michael M. Wolf. 2001

413 citations recorded by the source corpus.

We construct a set of ${2}^{{2}^{n}}$ independent Bell-correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that the inequalities are satisfied if and only if the correlations considered allow a local classical model. All these inequalities can be summarized in a single, albeit nonlinear inequality. We show that quantum correlations satisfy this condition provided the state has positive partial transpose with respect to any grouping of the n systems into two subsystems. We also provide an efficient algorithm for finding the maximal quantum-mechanical violation of each inequality, and show that the maximum is always attained for the generalized GHZ state.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/80d0c21fedd8d37551f1b7e34cf3ccad9875e6a9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Unbounded Violation of Tripartite Bell Inequalities (2007, background): “Whereas for two dichotomic observables per site the complete set of multipartite ‘full-correlation inequalities’ and their maximal violations within quantum mechanics is still known [75, 78], the case of more than two settings is, despite considerable effort [39, 50, 77], largely unexplored.”
Quantum Mechanics as a Theory of Probability (2005, background): “The witnesses that provide the maxumum value have a close relation to the facets of the correlation polytope for this case, see [42, 43].”
Multiphoton entanglement and interferometry (2008, background): “In 1990’s many proposals were made for observations of multi-photon entanglement (Żukowski et al., 1993; Żukowski, Zeilinger and Weinfurter (1995); Zeilinger et al., 1997; Pan and Zeilinger, 1998; see also section V.F.2), achieved this using single-photon detectors of a time resolution ˜70 ps, whi”
Entanglement detection (2008, background): “It turns out that the full set of such Bell inequalities can be generated and written down concisely in the form of a single nonlinear inequality [327,328].”