Unified picture for spatial, temporal and channel steering

TL;DR

This paper unifies the understanding of spatial, temporal, and channel quantum steering using Stinespring dilations, linking them to measurement incompatibility and establishing new inequalities and hierarchies.

Contribution

It introduces a unified framework for all three types of quantum steering, connecting them to measurement incompatibility and deriving tight steering inequalities.

Findings

Unified description of spatial, temporal, and channel steering

Link between steering and measurement incompatibility

Hierarchy between temporal steering and macrorealism

Abstract

Quantum steering describes how local actions on a quantum system can affect another, space-like separated, quantum state. Lately, quantum steering has been formulated also for time-like scenarios and for quantum channels. We approach all the three scenarios as one using tools from Stinespring dilations of quantum channels. By applying our technique we link all three steering problems one-to-one with the incompatibility of quantum measurements, a result formerly known only for spatial steering. We exploit this connection by showing how measurement uncertainty relations can be used as tight steering inequalities for all three scenarios. Moreover, we show that certain notions of temporal and spatial steering are fully equivalent and prove a hierarchy between temporal steering and macrorealistic hidden variable models.