  We discuss the analogy between topological entanglement and quantum
entanglement, particularly for tripartite quantum systems. We illustrate our
approach by first discussing two clearly (topologically) inequivalent systems
of three-ring links: The Borromean rings, in which the removal of any one link
leaves the remaining two non-linked (or, by analogy, non-entangled); and an
inequivalent system (which we call the NUS link) for which the removal of any
one link leaves the remaining two linked (or, entangled in our analogy). We
introduce unitary representations for the appropriate Braid Group ($B_3$) which
produce the related quantum entangled systems. We finally remark that these two
quantum systems, which clearly possess inequivalent entanglement properties,
are locally unitarily equivalent.
