Proving genuine multiparticle entanglement from separable nearest-neighbor marginals

Abstract

We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable, but where the entanglement can be proven using knowledge of a subset of the marginals only. Using an iteration of semidefinite programs we prove that for any possible marginal configuration up to six particles multiqubit states with the desired properties can be found. We then present a method to construct states with the same properties for more particles in higher dimensions.

9 pages, 5 figures, v2: final version

References in corpus (8)

• Entanglement detection
• Taming multiparticle entanglement
• Spin squeezing and entanglement
• Three-party pure quantum states are determined by two two-party reduced states
• Efficient device-independent entanglement detection for multipartite systems
• Bounding the set of classical correlations of a many-body system
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Cited by in corpus (10)

• Entanglement marginal problems
• Entanglement transitivity problems
• Fully non-positive-partial-transpose genuinely entangled subspaces
• Verifying genuine multipartite entanglement of the whole from its separable parts
• Minimal criteria for continuous-variable genuine multipartite entanglement
• Multipartite States under Elementary Local Operations
• Refuting spectral compatibility of quantum marginals
• Convicting emergent multipartite entanglement with evidence from a partially blind witness
• Uncertainty, von Neumann Entropy, and Squeezing in a Bipartite State of Two-Level Atoms
• Measure of tripartite quantum correlation in multiqubit symmetric pure state