Network Quantum Steering

TL;DR

This paper introduces the concept of network steering in quantum networks with independent sources, demonstrating novel activation effects and establishing conditions where network steering is impossible.

Contribution

It defines network steering and NLHS models, shows how Bell nonlocality and quantum steering results can demonstrate network steering, and provides no-go results for certain scenarios.

Findings

Network steering can be demonstrated using Bell nonlocality and quantum steering results.

Unsteerable states can exhibit network steering through entanglement swapping.

Explicit NLHS models show the absence of network steering in some scenarios.

Abstract

The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show how results from Bell nonlocality and quantum steering can be used to demonstrate network steering. We further show that it is a genuinely novel effect, by exhibiting unsteerable states that nevertheless demonstrate network steering, based upon entanglement swapping, yielding a form of activation. On the other hand, we provide no-go results for network steering in a large class of scenarios, by explicitly constructing NLHS models.