Hexapartite steering based on a four-wave-mixing process with a spatially structured pump

TL;DR

This paper investigates multipartite EPR steering in a six-beam four-wave-mixing process with a structured pump, revealing complex steering behaviors and monogamy relations, with implications for secure quantum networks.

Contribution

It introduces a matrix representation for steering analysis and explores type-IV monogamy relations within a novel four-wave-mixing scheme.

Findings

All (1+i)/(i+1)-mode steerings are explained by interaction strengths.

Strong collective five-mode steerings are achievable.

Type-IV monogamy relations are conditionally satisfied in this model.

Abstract

Multipartite Einstein-Podolsky-Rosen (EPR) steering has been widely studied, for realizing safer quantum communication. The steering properties of six spatially separated beams from the four-wave-mixing process with a spatially structured pump are investigated. Behaviors of all (1+i)/(i+1)-mode (i=1,2,3) steerings are understandable, if the role of the corresponding relative interaction strengths are taken into account. Moreover, stronger collective multipartite steerings including five modes also can be obtained in our scheme, which has potential applications in ultra-secure multiuser quantum networks when the issue of trust is critical. By further discussing about all monogamy relations, it is noticed that the type-IV monogamy relations, which are naturally included in our model, are conditionally satisfied. Matrix representation is used to express the steerings for the first time, which is very useful to understand the monogomy relations intuitively. Different steering properties obtained in this compact phase-insensitive scheme have potential applications for different kinds of quantum communication tasks.