Entanglement distillation from Greenberger-Horne-Zeilinger shares

TL;DR

This paper investigates how to convert distributed GHZ states into shared GHZ states among all parties using SLOCC transformations, revealing the optimal asymptotic rate based on bipartite log-ranks, generalizing matrix multiplication tensor results.

Contribution

It introduces a method to determine the optimal asymptotic rate for GHZ state distillation from multipartite states using bipartite log-rank measures, extending prior matrix tensor work.

Findings

Optimal asymptotic rate equals the minimum bipartite log-rank of the initial state.

Generalizes Strassen's result on matrix multiplication tensor to GHZ states.

Provides a framework for multipartite entanglement distillation analysis.

Abstract

We study the problem of converting a product of Greenberger-Horne-Zeilinger (GHZ) states shared by subsets of several parties in an arbitrary way into GHZ states shared by every party. Our result is that if SLOCC transformations are allowed, then the best asymptotic rate is the minimum of bipartite log-ranks of the initial state. This generalizes a result by Strassen on the asymptotic subrank of the matrix multiplication tensor.