Quantum Steering Ellipsoids

Abstract

The quantum steering ellipsoid of a two-qubit state is the set of Bloch vectors that Bob can collapse Alice's qubit to, considering all possible measurements on his qubit. We provide an elementary construction of the ellipsoid for arbitrary states, calculate its volume, and explain how this geometric representation can be made faithful. The representation provides a range of new results, and uncovers new features, such as the existence of "incomplete steering" in separable states. We show that entanglement can be analysed in terms of three geometric features of the ellipsoid, and prove that a state is separable if and only if it obeys a "nested tetrahedron" condition.

5+9 pages, 3+8 figures. v2: Re-organisation and improved notation, new discussion of possible extensions

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Cited by in corpus (117)

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• Quantum information as a non-Kolmogorovian generalization of Shannon's theory
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• Dynamics and recovery of genuine multipartite Einstein-Podolsky-Rosen steering and genuine multipartite nonlocality for a dissipative Dirac system via Unruh effect
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