Purification of multipartite entanglement by local operations

TL;DR

This paper presents a new recurrence protocol for purifying tripartite entanglement using local operations and classical communication, achieving higher yield and revealing novel types of tripartite entanglement.

Contribution

It introduces a genuine basis for tripartite states and demonstrates a purification protocol that surpasses previous methods in yield and efficiency.

Findings

Successful purification if initial fidelity > 0.4

Higher yield than previous protocols

Can produce bipartite Bell states when purification fails

Abstract

Multipartite entanglement purification is revisited by using the Local operations and classical communications(LOCCs). We demonstrate our idea by considering the tripartite case, i.e. the purification of tripartite entanglement. We express the general tripartite entangled states in a special representation of total spin operators $J_{123}^{2}$ and $% J_{12}^{2}$ of tripartite system with eigenvalues 15/4 and 2 respectively. This basis is a \textit{genuine basis} because it consists of of all the genuine entangled states of tripartite system. Our protocol is a recurrence one, and only two copies of the initial mixed tripartite entangled states are needed in each round. It is shown that if the initial fidelity is larger than a threshold 0.4, the purification process will succeed.The yield of the current protocol is higher than the previous multipartite entanglement purification protocols. As a by-product, we can get a bipartite pure Bell state when the purification protocol fails for W state. Our protocol also shows that there may be some special kind of tripartite entanglement which belongs to neither W-type entanglement nor GHZ-type entanglement.