Quantification of quantum steering in a Gaussian Greenberger-Horne-Zeilinger state

TL;DR

This paper fully quantifies bipartite EPR steering in a Gaussian tripartite GHZ state, revealing unique steerability properties and demonstrating one-way steering, with implications for quantum secret sharing and multiparty quantum information.

Contribution

It introduces a method to quantify bipartite steering in Gaussian GHZ states and uncovers their unique steerability properties, including one-way steering and monogamy relations.

Findings

No (1+1)-mode steerability in tripartite GHZ state

Existence of collective steerability between (1+2) and (2+1) modes

Experimental verification of monogamy relations for Gaussian steerability

Abstract

As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. Greenberger-Horne-Zeilinger (GHZ) state plays important role in quantum communication network. By reconstructing the covariance matrix of a continuous variable tripartite GHZ state, we fully quantify the amount of bipartite steering under Gaussian measurements. We demonstrate that the (1+1)-mode steerability is not exist in the tripartite GHZ state, only the collectively steerability exist between the (1+2)-mode and (2+1)-mode partitions. These properties confirm that the tripartite GHZ state is a perfect resource for quantum secret sharing protocol. We also demonstrate one-way EPR steering of the GHZ state under Gaussian measurements, and experimentally verify the introduced monogamy relations for Gaussian steerability. Our experiment provides reference for using EPR steering in Gaussian GHZ states as a valuable resource for multiparty quantum information tasks.