Einstein-Podolsky-Rosen steering in Gaussian weighted graph states

TL;DR

This paper investigates Einstein-Podolsky-Rosen (EPR) steering in Gaussian weighted graph states, revealing how weight factors influence steering properties and demonstrating its potential as a resource for multiparty quantum communication.

Contribution

It introduces the analysis of EPR steering in Gaussian weighted graph states, including new findings on steering dependence on weights and monogamy relations, extending previous cluster state studies.

Findings

Gaussian EPR steering depends on weight factors in the graph state

EPR steering exists between certain modes in weighted states but not in cluster states

Steering obeys Coffman-Kundu-Wootters monogamy relation

Abstract

Einstein-Podolsky-Rosen (EPR) steering, as one of the most intriguing phenomenon of quantum mechanics, is a useful quantum resource for quantum communication. Understanding the type of EPR steering in a graph state is the basis for application of it in a quantum network. In this paper, we present EPR steering in a Gaussian weighted graph state, including a linear tripartite and a four-mode square weighted graph state. The dependence of EPR steering on weight factor in the weighted graph state is analyzed. Gaussian EPR steering between two modes of a weighted graph state is presented, which does not exist in the Gaussian cluster state (where the weight factor is unit). For the four-mode square Gaussian weighted graph state, EPR steering between one and its two nearest modes is also presented, which is absent in the four-mode square Gaussian cluster state. We also show that Gaussian EPR steering in a weighted graph state is also bounded by the Coffman-Kundu-Wootters monogamy relation. The presented results are useful for exploiting EPR steering in a Gaussian weighted graph state as a valuable resource in multiparty quantum communication tasks.