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arXiv · 1407.8440

Geometric representation of two-qubit entanglement witnesses

Antony Milne·David Jennings·Terry Rudolph
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Abstract

Any two-qubit state can be represented geometrically by a steering ellipsoid inside the Bloch sphere. We extend this approach to represent any block positive two-qubit operator $B$. We derive a novel classification scheme based on the positivity of $\det B$ and $\det B^\mathrm{T_B}$; this shows that any ellipsoid inside the Bloch sphere must represent either a two-qubit state or a two-qubit entanglement witness. We focus on such witnesses and their corresponding ellipsoids, finding that properties such as witness optimality are naturally manifest in this geometric representation.

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Antony Milne, David Jennings, Terry Rudolph. 2015-07-10. Geometric representation of two-qubit entanglement witnesses. https://doi.org/10.1103/physreva.92.012311

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