Tripartite Entanglement: Foundations and Applications

We review some current ideas of tripartite entanglement. In particular, we consider the case representing the next level of complexity beyond the simplest (though far from trivial) one, namely the bipartite case. This kind of entanglement plays an essential role in understanding the foundations of quantum mechanics. It also allows for implementing several applications in the fields of quantum information processing and quantum computing. In this paper, we review the fundamental aspects of tripartite entanglement focusing on Greenberger–Horne–Zeilinger and W states for discrete variables. We discuss the possibility of using it as a resource to execute quantum protocols and present some examples in detail.