Higher dimensional entanglement without correlations

TL;DR

This paper demonstrates that higher-dimensional quantum systems (qudits) can exhibit genuine multipartite entanglement without involving correlations among all particles, challenging traditional notions of entanglement.

Contribution

It provides the first examples of higher-dimensional states with genuine multipartite entanglement supported only by fewer-than-N particle correlations.

Findings

Genuine N-partite entanglement can exist without N-particle correlations in qudits.

Constructed states differ from qubit cases, expanding understanding of entanglement.

These states serve as test-beds for quantifying multipartite quantum 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.