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When two qubits A and B are in an appropriate state, Alice can remotely steerBob's system B into different ensembles by making different measurements on A.This famous phenomenon is known as quantum steering, or Einstein-Podolsky-Rosensteering. Importantly, quantum steering establishes the correspondence not onlybetween a measurement on A (made by Alice) and an ensemble of B (owned by Bob)but also between each of Alice's measurement outcomes and an unnormalizedconditional state of Bob's system. The unnormalized conditional states of Bcorresponding to all possible measurement outcomes of Alice are called Alice'ssteering outcomes. We show that, surprisingly, the $4$-dimensional geometry ofAlice's steering outcomes completely determines both the non-separability ofthe two-qubit state and its steerability from her side. Consequently, theproblem of classifying two-qubit states into non-separable and steerableclasses is equivalent to geometrically classifying certain $4$-dimensionalskewed double-cones.

Non-separability and steerability of two-qubit states from the geometry of steering outcomes