Spooky action-at-a-distance in general probabilistic theories

We call a probabilistic theory “complete” if it cannot be further refined by no-signaling hidden-variable models, and name a theory “spooky” if every equivalent hidden-variable model violates Shimonyʼs Outcome Independence. We prove that a complete theory is spooky if and only if it admits a pure steering state in the sense of Schrödinger. Finally we show that steering of complementary states leads to a Schrödingerʼs-cat-like paradox.