title: 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 analyzed 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.
authors: Mathematical Sciences, John Crank 501, Brunel University, Uxbridge UB8 3PH, United Kingdom and Controlled Quantum Dynamics Theory, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom.
authors: Sania
authors: S
authors: Jevtic
authors: Controlled Quantum Dynamics Theory, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom and Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2 L 2Y5, Canada.
authors: Matthew
authors: M
authors: Pusey
authors: Controlled Quantum Dynamics Theory, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom.
authors: David
authors: D
authors: Jennings
authors: Controlled Quantum Dynamics Theory, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom.
authors: Terry
authors: T
authors: Rudolph