Multipartite fully entangled fraction

TL;DR

This paper introduces the multipartite fully entangled fraction (MFEF), a measure of how close a quantum state is to GHZ states, generalizing the bipartite fully entangled fraction and enabling efficient numerical computation.

Contribution

It generalizes the fully entangled fraction to multipartite states and provides a method to compute MFEF via finite-order polynomial equations.

Findings

MFEF measures closeness to GHZ states in multipartite systems

Analytical expressions are complex, but numerical computation is feasible

MFEF is determined by finite-order polynomial equations

Abstract

Fully entangled fraction is a definition for bipartite states, which is tightly related to bipartite maximally entangled states, and has clear experimental and theoretical significance. In this work, we generalize it to multipartite case, we call the generalized version multipartite fully entangled fraction (MFEF). MFEF measures the closeness of a state to GHZ states. The analytical expressions of MFEF are very difficult to obtain except for very special states, however, we show that, the MFEF of any state is determined by a system of finite-order polynomial equations. Therefore, the MFEF can be efficiently numerically computed.