Activation of quantum steering sharing with unsharp nonlocal product measurements

Unsharp measurements are commonly employed for sharing quantum steering among multiple observers, but they are currently restricted to local measurements and unsuitable for nonlocal-measurement-based tasks. In this work, we propose an effective method for constructing optimal nonlocal measurements using quantum ellipsoids to share quantum steering. This method is applicable to any bipartite state and advantageous even when the number of measurement settings is large. Taking the Greenberger-Horne-Zeilinger state as an example, we demonstrate that unsharp nonlocal product measurements can activate steering sharing compared with local measurements. Furthermore, our results indicate that the activation ability of unequal-strength nonlocal measurements is stronger than that of equal-strength ones. Unlike previous activation methods, ours does not require increasing the copy number of the shared states or weakening other types of quantum correlations, making it both experiment-friendly and resource-reusable.