Topologically noise robust network steering without inputs

TL;DR

This paper introduces a topologically noise-robust method for network steering in quantum networks without inputs, using linear witnesses to detect swap-steering and self-test states, applicable to ring networks with arbitrary nodes.

Contribution

It presents the first topologically robust, noise-tolerant approach to observe steerability without network structure assumptions and demonstrates quantum advantage in such networks.

Findings

Proposed linear witness detects triangle network swap-steering.

Achieved self-testing of states and measurements in the network.

Extended framework to ring networks with arbitrary nodes.

Abstract

Quantum networks with independent sources allow observing quantum nonlocality or steering with just a single measurement per node of the network, or without any inputs. Inspired by the recently introduced notion of swap-steering, we consider here the triangle network scenario without inputs, where one of the parties is trusted to perform a well-calibrated measurement. In this scenario, we first propose a linear witness to detect triangle network swap-steering. Then, by using the correlations that achieve the maximum value of this inequality, and assuming that all the sources are the same, we can self-test the state generated by the sources and the measurements of the untrusted party. We then extend this framework to ring networks with an arbitrary number of nodes with one of them being trusted. Interestingly, this is the first example of a topologically robust, that is, one can observe steerability without assuming the network structure of the network, as well as noise-robust quantum advantage in a network. Additionally, by allowing the trusted party to perform tomography of their subsystems, we demonstrate that every bipartite entangled state will result in swap-steerable correlations in the ring network. For this purpose, we construct linear witnesses to detect ring network swap-steering corresponding to every bipartite entangled state.