Figure 1
From: Discrimination of two-qubit unitaries via local operations and classical communication
A convex hull in Eq. (11) of the spectrum of a unitary transformation is shown.
Vertices A, B, C and D correspond to 
, 
, 
and 
, respectively, since λ4 ≥ λ1 ≥ λ2 ≥ λ3. Any point in the convex hull can be reached by manipulating input state in Eq. (8). For instance, by taking an input state as Bell states, 
for j = 1, 2, 3, 4, vertices A, B, C and D can be reached. In (a) the convex hull contains the origin and there exists an input state such that perfect discrimination is achieved. In (b) the fidelity F corresponds to the distance between the convex hull and the origin, see Eq. (12).
