Channel Steering

TL;DR

This paper extends the concept of quantum steerability from bipartite states to quantum channels, emphasizing coherence of channel extensions and connecting it with local operations and classical communication.

Contribution

It introduces a novel notion of steerability for channels, differentiates it from state steerability, and develops measures for quantifying channel steerability.

Findings

Steerability of channels relates to coherence of channel extensions.

The approach generalizes state steerability using the Choi-Jamiolkowski isomorphism.

Measures for channel steerability are proposed.

Abstract

We introduce and study the notion of steerability for channels. This generalizes the notion of steerability of bipartite quantum states. We discuss a key conceptual difference between the case of states and the case of channels: while state steering deals with the notion of "hidden" states, steerability in the channel case is better understood in terms of coherence of channel extensions, rather than in terms of "hidden" channels. This distinction vanishes in the case of states. We further argue how the proposed notion of lack of coherence of channel extensions coincides with the notion of channel extensions realized via local operations and classical communication. We also discuss how the Choi-Jamiolkowski isomorphism allows the direct application of many results about states to the case of channels. We introduce measures for the steerability of channel extensions.