Sharing Asymmetric Einstein-Podolsky-Rosen Steering with Projective Measurements

Abstract: Recently, both global and local classical randomness-assisted projective measurement protocols have been employed to share Bell nonlocality of an entangled state among multiple sequential parties. Unlike Bell nonlocality, Einstein-Podolsky-Rosen (EPR) steering exhibits distinct asymmetric characteristics and serves as the necessary quantum resource for one-sided device-independent quantum information tasks. In this work, we propose a projective measurement protocol and investigate the shareability of EPR steering with steering radius criterion theoretically and experimentally. Our results reveal that arbitrarily many independent parties can share one-way steerability using projective measurements, even when no shared randomness is available. Furthermore, by leveraging only local randomness, asymmetric two-way steerability can also be shared. Our work not only deepens the understanding of the role of projective measurements in sharing quantum correlations but also opens up a new avenue for reutilizing asymmetric quantum correlations.