Detecting quantum steering in networks

Quantum networks promise an unprecedented leap in semi-device-independent communication and security by capitalizing on quantum steering. However, current methods for assessing quantum network steering are constrained to specific cases. In this work, we introduce the network-Clauser-Horn-Shimony-Holt-like inequality for investigating network steering independent of entanglement source characteristics. We employ this inequality to detect full network steering in both single-node and multinode repeater networks and assess the tolerance of various noise models. Under a specific noise model, our method is used to compute the bound of semi-device-independent communication distance. Through case studies, we also demonstrate that our method, as a semi-device-independent entanglement witness, is more suitable for settings requiring Bell measurements compared to network Bell inequality. These findings open new avenues for broader ways to detect quantum steering independent of entanglement sources.