Quantum Steering Ellipsoids

TY - JOUR

T1 - Quantum Steering Ellipsoids

AU - Jevtic, Sania

AU - Pusey, Matthew F.

AU - Jennings, David

AU - Rudolph, Terry

PY - 2014/7/8

Y1 - 2014/7/8

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevLett.113.020402

DO - 10.1103/PhysRevLett.113.020402

M3 - Article

SN - 0031-9007

VL - 113

JO - Physical Review Letters

JF - Physical Review Letters

M1 - 020402

ER -