Several kinds of Gaussian quantum channels related to Einstein-Podolsky-Rosen steering

TL;DR

This paper classifies and analyzes various Gaussian quantum channels related to Einstein-Podolsky-Rosen steering, providing conditions for their properties and exploring their interrelations.

Contribution

It introduces new classes of Gaussian channels associated with quantum steering and characterizes their properties and relationships in continuous-variable quantum systems.

Findings

Derived necessary and sufficient conditions for Gaussian channels to be steering-annihilating, breaking, or unsteerable.

Provided a detailed characterization of Gaussian unsteerable superchannels.

Explored the intrinsic relationships among different classes of Gaussian steering-related channels.

Abstract

Quantum steering is a crucial quantum resource that lies intermediate between entanglement and Bell nonlocality. Gaussian channels, meanwhile, play a foundational role in diverse quantum protocols, secure communication, and related fields. In this paper, we focus on several classes of Gaussian channels associated with quantum steering: Gaussian steering-annihilating channels, Gaussian steering-breaking channels, Gaussian unsteerable channels, and maximal Gaussian unsteerable channels. We give the concepts of these channels, derive the necessary and sufficient conditions for a Gaussian channel to belong to each class, and explore the intrinsic relationships among them. Additionally, since quantifying the steering capability of Gaussian channels in continuous-variable systems requires an understanding of the structure of free superchannels, we also provide a detailed characterization of Gaussian unsteerable superchannels and maximal Gaussian unsteerable superchannels.