Quantifying Einstein-Podolsky-Rosen steering

Abstract

Einstein-Podolsky-Rosen steering is a form of bipartite quantum correlation that is intermediate between entanglement and Bell nonlocality. It allows for entanglement certification when the measurements performed by one of the parties are not characterized (or are untrusted) and has applications in quantum key distribution. Despite its foundational and applied importance, Einstein-Podolsky-Rosen steering lacks a quantitative assessment. Here we propose a way of quantifying this phenomenon and use it to study the steerability of several quantum states. In particular, we show that every pure entangled state is maximally steerable and the projector onto the antisymmetric subspace is maximally steerable for all dimensions; we provide a new example of one-way steering and give strong support that states with positive-partial transposition are not steerable.