Quantifying the Operational Cost of Multipartite Entanglement

TL;DR

This paper introduces a universal method to quantify multipartite entanglement in quantum systems, linking the entanglement measure to the experimental cost of creating such states, and provides analytical calculations for specific classes.

Contribution

It presents a novel approach to quantify k-partite entanglement by maximizing bipartite measures, connecting entanglement to experimental resource costs, and analytically evaluates the entanglement of formation for various states.

Findings

The method classifies multipartite states based on their entanglement cost.

Creating a k-partite entangled state requires at least k-1 two-particle gates.

Analytical formulas for k-partite entanglement of formation are derived for W states.

Abstract

Multipartite entanglement determines the strength and range of interactions in many-body quantum systems. Yet, it is hard to evaluate it, due to the complex structures of quantum states. Here, we introduce a generic method to quantify the k <= N-partite entanglement of an N-particle system, by maximizing an arbitrary bipartite entanglement measure within subsystems of size up to k. The resulting classification of multipartite states captures their experimental cost: creating a k-partite entangled state requires at least k-1 two-particle entangling gates. Further, we analytically calculate the newly defined k-partite entanglement of formation, which generalizes an important bipartite entanglement measure, in several classes of states, including the W states of any dimension.