Random multiparty entanglement distillation

TL;DR

This paper investigates the process of random distillation of multiparty entangled states, demonstrating its advantages for certain states like W-class and Dicke states, but not for multiple copies of pure states.

Contribution

It provides a rigorous definition of advantageous random distillation and analyzes its effectiveness across different classes of multiparty entangled states.

Findings

Random distillation is always advantageous for W-class three-qubit states.

It is sometimes advantageous for GHZ-class states.

Random distillation is not advantageous for multiple copies of pure states.

Abstract

We describe various results related to the random distillation of multiparty entangled states - that is, conversion of such states into entangled states shared between fewer parties, where those parties are not predetermined. In previous work [Phys. Rev. Lett. 98, 260501 (2007)] we showed that certain output states (namely Einstein-Podolsky-Rosen (EPR) pairs) could be reliably acquired from a prescribed initial multipartite state (namely the W state) via random distillation that could not be reliably created between predetermined parties. Here we provide a more rigorous definition of what constitutes ``advantageous'' random distillation. We show that random distillation is always advantageous for W-class three-qubit states (but only sometimes for Greenberger-Horne-Zeilinger (GHZ)-class states). We show that the general class of multiparty states known as symmetric Dicke states can be readily converted to many other states in the class via random distillation. Finally we show that random distillation is provably not advantageous in the limit of multiple copies of pure states.