Dicke states: production from EPR pairs and entanglement analysis

Abstract

In this work we analyze the problem of creation of Dicke states through the process of entanglement swapping. First we deal with the tripartite case, presenting a deterministic protocol based on a source of EPR pairs. Still in this topic we show that it is possible to create perfect W states (tripartite Dicke states), even when the EPR source does not yield maximally entangled pairs, with a finite success rate. Subsequently we cope with the n-partite case, for which we present a probabilistic procedure, also employing EPR-pair sources, where the output, whenever successful, is perfect. The analysis of this protocol reveals a critical transition for the success probability, which is characterized in the framework of Landau theory of second order phase-transitions. Finally we proceed with a study of the entanglement between bipartitions of systems described by Dicke states, which allows for the implementation of entanglement witnesses. For each Dicke state we present a highly sensitive witness.