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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.
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Discord can be calculated analytically when θ = 0 , π 2 \theta=0,\frac{\pi}{2} , and at these points ρ \rho is an X-state [ 18 ] and this agrees with our findings
Cited in the paper.
More formally, it was shown [ 20 , 21 ] that every convex body in ℝ n \mathbb{R}^{n} Euclidean space contains a unique maximal volume ellipsoid, and that a Euclidean ball is that maximum if and only if there exist vectors { 𝒙 k } \{\bm{x}_{k}\} in the set of contact points of the ball with the convex body, and positive numbers { c k } \{c_{k}\} such that ∑ k c k 𝒙 k = 0 \sum\displaylimits_{k}c_{k}\bm{x}_{k}=0 and ∑ k c k 𝒙 k T 𝒙 k = r 2 𝟙 \sum\displaylimits_{k}c_{k}\bm{x}^{T}_{k}\bm{x}_{k}=r^{2}\mathbbm{1} , where r r is the radius of the ball. Inspection of the in-sphere for the regular tetrahedron in the Bloch sphere shows that is is the case for { 𝒙 k } \{\bm{x}_{k}\} being the four intersection points
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