Borromean Entanglement of the GHZ State

Abstract

In this paper, I will point out some curious connections between entangled quantum states and classical knot configurations. In particular, I will show that the entanglement of the particles in a Greenberger-Horne-Zeilingerl (GHZ) state is modelled by a set of interlinked rings known as the Borromean rings. It is widely acknowledged that the non-local properties of multiparticle quantum states (such as the GHZ state) derive from their entanglement. By the entanglement of a multiparticle state, I mean simply that the wave function of the state cannot be written as a product of wave functions of the individual particles. Now one of the images conjured up by the term “entanglement” is that of a tangled collection of strings. This led me to enquire whether there might be any similarities between the entanglement of quantum particles and the entanglement of loops of string, or whether the expectation of such a connection is completely far-fetched.