Activation of quantum steering sharing with unsharp nonlocal product measurements

Abstract: Quantum steering is commonly shared among multiple observers by utilizing unsharp measurements. However, their usage is limited to local measurements and is not suitable for nonlocal-measurement-based cases. Here, we present a novel approach in this study, suggesting a highly efficient technique to construct optimal nonlocal measurements by utilizing quantum ellipsoids to share quantum steering. This technique is suitable for any bipartite state and offers benefits even in scenarios with a high number of measurement settings. Using the Greenberger-Horne-Zeilinger state as an illustration, we show that employing unsharp nonlocal product measurements can activate the phenomenon of steering sharing in contrast to using local measurements. Moreover, our findings demonstrate that nonlocal measurements with unequal strength possess a greater activation capability compared to those with equal strength. Our activation method differs from previous ones as it eliminates the need to copy the shared states or diminish other quantum correlations, thus making it convenient for practical experimentation and conservation of resources.