N-particle nonclassicality without N-particle correlations

Abstract

Most of known multipartite Bell inequalities involve correlation functions for all subsystems. They are useless for entangled states without such correlations. We give a method of derivation of families of Bell inequalities for N parties, which involve, e.g., only (N-1)-partite correlations, but still are able to detect proper N-partite entanglement. We present an inequality which reveals five-partite entanglement despite only four-partite correlations. Classes of inequalities introduced here can be put into a handy form of a single non-linear inequality. An example is given of an N qubit state, which strongly violates such an inequality, despite having no N-qubit correlations. This surprising property might be of potential value for quantum information tasks.

5 pages

References in corpus (5)

• Experimental entanglement of a six-photon symmetric Dicke state
• Quantum Correlation Without Classical Correlations
• Explicit form of correlation function three-settings tight Bell inequalities for three qubits
• More non-locality in the three-qubit Greenberger-Horne-Zeilinger state
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Cited by in corpus (9)

• Detecting non-locality in multipartite quantum systems with two-body correlation functions
• Nonlocality in many-body quantum systems detected with two-body correlators
• Genuine Multipartite Entanglement without Multipartite Correlations
• Detecting genuine multipartite entanglement of pure states with bipartite correlations
• Shareability of Quantum Steering and its Relation with Entanglement
• Complementarity between Tripartite Quantum Correlation and Bipartite Bell Inequality Violation in Three Qubit States
• Genuine $N$-partite entanglement without $N$-partite correlation functions
• Genuinely entangled symmetric states with no $N$-partite correlations
• Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies