Statistical correlators and tripartite entanglement

Abstract

It has recently been argued that among the various suggested measures of tripartite entanglement, the two particular measures, viz. the Concurrence Fill and the Genuine Multipartite Concurrence, are the only ‘genuine’ tripartite entanglement measures based on certain suitably specified criteria. In this context, we show that these two genuine tripartite entanglement measures can be empirically determined for the two important classes of tripartite entangled states, viz. the generalized GHZ and the generalized W states using the derived relationships of these two measures with the observable statistical correlators like the Pearson correlator and mutual information. Such a formulated scheme would therefore provide for the first time the means to exactly quantify tripartite entanglement, crucial for the proper assessment of its efficacy as resource. We also point out two specific applications of this scheme, viz. (a) enabling empirical demonstration of the potentially significant feature of inequivalence between Concurrence Fill and Genuine Multipartite Concurrence in quantitatively assessing which of the two given tripartite states is more entangled than the other one and (b) enabling experimental detection of the recently predicted phenomenon of entanglement sudden death for a tripartite system.