Figure 3
From: Discrimination of two-qubit unitaries via local operations and classical communication
Suppose that resulting two states 
and 
are not orthogonal and do not lead to perfect discrimination between two unitary transformations.
(a) The fidelity is given by the distance between origin and the convex hull, see also Eq. (12). (b) The local convex hull constructed by a product state is found as □PQRS where {P, Q, R, S} are midpoints of {DA, AB, BC, CD}, respectively. Note that, while an input state is prepared locally, discrimination between resulting states is performed by global operations. Then, the distance between the local convex hull and the origin corresponds to the distance OS, since OS is orthogonal to DC and gives the minimal distance between the local convex hull and the origin.
