Higher dimensional entanglement without correlations

Abstract

It has been demonstrated both theoretically and experimentally that genuine multipartite entanglement between qubits can exist even in the absence of multipartite correlations. Here we provide first examples of this effect in higher dimensional systems -- qudits. We construct states in which genuine $N$-partite entanglement between qudits is supported only by correlations involving strictly less than $N$ particles. The construction differs in several aspects from the ones for qubits. The states introduced here are a natural test-bed for candidate quantifiers of genuinely multipartite quantum correlations.

arXiv comment6 pages, 1 figure

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Cited by in corpus (9)

• Analysing quantum systems with randomised measurements
• Characterizing quantum states via sector lengths
• Maximum $N$-body correlations do not in general imply genuine multipartite entanglement
• $k$-uniform mixed states
• An approach to constructing genuinely entangled subspaces of maximal dimension
• Criteria to detect genuine multipartite entanglement using spin measurements
• A Moment for Random Measurements
• Cooperation and dependencies in multipartite systems
• Testing Genuine Multipartite Nonlocality via an Inflated Network with Multi-copy Entangled States