Bell inequality with an arbitrary number of settings and its applications

Abstract

Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results. Moreover, a necessary and sufficient condition for the violation of this inequality is presented. It turns out that the class of non-separable states which do not admit local realistic description is extended when compared to the two-setting inequalities. However, supporting the conjecture of Peres, quantum states with positive partial transposes with respect to all subsystems do not violate the inequality. Additionally, we follow a general link between Bell inequalities and communication complexity problems, and present a quantum protocol linked with the inequality, which outperforms the best classical protocol.

arXiv comment8 pages, To appear in Phys. Rev. A

References in corpus (15)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• All multipartite Bell correlation inequalities for two dichotomic observables per site
• Bell's theorem for general N-qubit states
• Violation of Bell's inequality: criterion for quantum communication complexity advantage
• Quantum Communication between N partners and Bell's inequalities
• Multipartite bound entangled states that violate Bell's inequality
• Do all pure entangled states violate Bell's inequalities for correlation functions?
• Bell's inequalities for states with positive partial transpose
• Experimental quantum communication complexity
• Functional Bell inequalities can serve as a stronger entanglement witness
• Better detection of Multipartite Bound Entanglement with Three-Setting Bell Inequalities
• On Series of Multiqubit Bell's Inequalities
• Classification of mixed high-dimensional multiparticle systems

Cited by in corpus (17)

• Entanglement detection
• Unbounded violation of tripartite Bell inequalities
• Multi-setting Bell inequality for qudits
• Multisetting Bell-type inequalities for detecting genuine tripartite entanglement
• Non-classicality thresholds for multiqubit states - numerical analysis
• Genuine Multipartite Entanglement without Multipartite Correlations
• NMR Analog of Bell's Inequalities Violation Test
• Entanglement and communication-reducing properties of noisy N-qubit states
• Robust Bell inequalities from communication complexity
• Unmasking the Polygamous Nature of Quantum Nonlocality
• Multipartite bound entanglement and multi-setting Bell inequalities
• Multipartite positive-partial-transpose inequalities exponentially stronger than local reality inequalities
• Multisetting Bell inequalities for $N$ spins-1 avoiding KS contradiction
• Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies
• Multisetting protocol for Bell correlated states detection with spin-$f$ systems
• How Likely Are You to Observe Non-locality with Imperfect Detection Efficiency and Random Measurement Settings?
• The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy