# Swapping of Gaussian Einstein-Podolsky-Rosen steering

## TL;DR

This paper introduces two entanglement swapping schemes for Gaussian EPR steering, demonstrating extended transmission distances, one-way steering, and steering direction changes, advancing secure quantum communication techniques.

## Contribution

It presents novel single-channel and dual-channel swapping schemes for Gaussian EPR steering, including analysis of their transmission distances and steering direction dynamics.

## Key findings

- Single-channel scheme achieves longer transmission distance.
- One-way EPR steering can occur after swapping over lossy channels.
- Steering direction can change in dual-channel scheme.

## Abstract

Einstein-Podolsky-Rosen (EPR) steering is a quantum mechanical phenomenon that allows one party to steer the state of a distant party by exploiting their shared entanglement. It has potential applications in secure quantum communication. In this paper, we present two swapping schemes of Gaussian EPR steering, single-channel and dual-channel schemes, by the technique of entanglement swapping. Two space-separated independent EPR steering states without a direct interaction present EPR steering after deterministic swapping. By comparing the EPR steering of the single-channel and dual-channel schemes, we show that the transmission distance of the single-channel scheme is much longer than that of the symmetric dual-channel scheme. Different from entanglement swapping, one-way EPR steering is presented after swapping over lossy channels. The most interesting thing is that the change of the EPR steering direction is observed in the dual-channel scheme. We also show that excess noise in a quantum channel will shorten the transmission distance of the swapping, even leading to the sudden death of EPR steering. The presented schemes provide a technical reference for remote quantum communications with EPR steering.