Configuration of separability and tests for multipartite entanglement in Bell-type experiments

Abstract

We derive tight quadratic inequalities for all kinds of hybrid separable-inseparable $n$-particle density operators on an arbitrary dimensional space. This methodology enables us to truly derive a tight quadratic inequality as tests for full $n$-partite entanglement in various Bell-type correlation experiments on the systems that may not be identified as a collection of qubits, e.g., those involving photons measured by incomplete detectors. It is also proved that when the two measured observables are assumed to precisely anti-commute, a stronger quadratic inequality can be used as a witness of full $n$-partite entanglement.

To appear in Phys. Rev. Lett. (submitted on Jul. 4, 2002)

References in corpus (11)

• Observation of three-photon Greenberger-Horne-Zeilinger entanglement
• Experimental Four-photon Entanglement and High-fidelity Teleportation
• All multipartite Bell correlation inequalities for two dichotomic observables per site
• Bell-type inequalities to detect true n-body non-separability
• Classification of multi-qubit mixed states: separability and distillability properties
• Bell inequality, Bell states and maximally entangled states for n qubits
• Bell-type inequalities for partial separability in N-particle systems and quantum mechanical violations
• Sufficient conditions for three-particle entanglement and their tests in recent experiments
• Quadratic Bell inequalities as tests for multipartite entanglement
• Bell's inequalities for states with positive partial transpose
• Observables suitable for restricting the fidelity to multipartite maximally entangled states

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• "All-versus-nothing" proof of genuine tripartite steering and entanglement certification in the two-sided device-independent scenario
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