Geometric representation of two-qubit entanglement witnesses
Antony Milne, David H. Jennings, Terry Rudolph · Physical Review A · 2015
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 classification scheme based on the positivity of $detB$ and $det{B}^{{\mathrm{T}}_{\mathrm{B}}}$; 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.