Statistical Correlators and Tripartite Entanglement

TL;DR

This paper proposes a method to empirically quantify tripartite entanglement in quantum states using observable statistical correlators, enabling practical assessment and comparison of entanglement measures.

Contribution

It introduces a scheme to determine Concurrence Fill and Genuine Multipartite Concurrence from observable correlators for GHZ and W states, advancing experimental quantification of tripartite entanglement.

Findings

Empirical relationships established between entanglement measures and correlators.

First-time exact quantification of tripartite entanglement using observable data.

Potential to experimentally observe entanglement sudden death.

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. b) Enabling experimental detection of the recently predicted phenomenon of entanglement sudden death for a tripartite system.