Several kinds of Gaussian quantum channels
Ruifen Ma, Yanjing Sun, Xiaofei Qi
TL;DR
The paper investigates how Gaussian channels influence EPR steering in continuous-variable systems by classifying Gaussian steering-annihilating, steering-breaking, and maximal Gaussian unsteerable channels and deriving their necessary and sufficient criteria. It then develops a Gaussian steering resource-theory perspective by characterizing Gaussian unsteerable and maximal Gaussian unsteerable superchannels as free operations, with formal composition rules and matrix-inequality conditions. The results provide operational tools to quantify and manipulate steering under Gaussian dynamics, including exact conditions for keeping or destroying steering and for preserving unsteerability under Gaussian superchannels. This advances CV quantum information by enabling systematic control of steering via Gaussian processes and informs secure CV communications and related protocols.
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.