Figure 1

(a) Planes in the Poincaré Sphere defined by a constant value of \({\text{S}}_{1}\). The plane that contains the input state \({\mathbf{S}}_{in}\) defines all the possible SoPs that the effective state \(\langle{\mathbf{S}}_{e}\rangle\) can reach. Note that only the plane \({\text{S}}_{1} = 0\) contains all the possible DoP values. (b,c) Composition of the effective output state \(\langle{\mathbf{S}}_{e}\rangle\) as the incoherent addition of states \({\mathbf{S}}_{A}\) and \({\mathbf{S}}_{B}\) for an input state with \(S_{in 1} = 0\) when \(\cos \overline{\delta } > 0\) (b) and when \(\cos \overline{\delta } < 0\) (c).