# Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states

## TL;DR

This paper experimentally demonstrates the distribution and monogamy constraints of EPR steering in Gaussian cluster states, highlighting their potential for secure multiparty quantum communication.

## Contribution

It provides the first experimental verification of monogamy relations for Gaussian EPR steering in cluster states, including one-way and multi-mode steering.

## Key findings

- Verified monogamy relations for Gaussian steerability
- Demonstrated one-way EPR steering in cluster states
- Observed complex steering distribution patterns

## Abstract

Understanding how quantum resources can be quantified and distributed over many parties has profound applications in quantum communication. As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. By reconstructing the covariance matrix of a continuous variable four-mode square Gaussian cluster state subject to asymmetric loss, we quantify the amount of bipartite steering with a variable number of modes per party, and verify recently introduced monogamy relations for Gaussian steerability, which establish quantitative constraints on the security of information shared among different parties. We observe a very rich structure for the steering distribution, and demonstrate one-way EPR steering of the cluster state under Gaussian measurements, as well as one-to-multi-mode steering. Our experiment paves the way for exploiting EPR steering in Gaussian cluster states as a valuable resource for multiparty quantum information tasks.