Quantum steering ellipsoids, extremal physical states and monogamy

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Milne, Antony
Jevtic, Sania
Jennings, David
Wiseman, Howard
Rudolph, Terry
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2014
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Abstract

Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit state. We give necessary and sufficient conditions for when the geometric data describe a physical state and investigate maximal volume ellipsoids lying on the physical-unphysical boundary. We derive monogamy relations for steering that are strictly stronger than the Coffman-Kundu-Wootters (CKW) inequality for monogamy of concurrence. The CKW result is thus found to follow from the simple perspective of steering ellipsoid geometry. Remarkably, we can also use steering ellipsoids to derive non-trivial results in classical Euclidean geometry, extending Euler's inequality for the circumradius and inradius of a triangle.

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New Journal of Physics

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16

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© The Author(s) 2014. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the authors and the title of the work, journal citation and DOI.

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Physical sciences

Quantum information, computation and communication

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