In our recent paper [1], Eq. (54) for the transformation of a c-matrix (the c-vector $\mathbf{c}$ written in matrix form) by a system is not valid. This can be seen from the results of the appendix of that paper, which would mean that if the first line of Eq. (54) were true, the Mueller matrix for a deterministic system would be expressible as the outer product of a matrix and its complex conjugate, which is not in general true. In fact, recently it has been shown that a deterministic Mueller matrix can be written as the matrix product of a $4\times 4$ matrix, the $Z$-matrix (polarization coupling matrix, or state generating matrix), and its complex conjugate, $\mathbf{M}=\frac{1}{2}{\mathbf{ZZ}}^{*}$ in our notation [2,3].

In addition, there was also a typographical error in part of Eq. (20) [1], which should have read ${\mathbf{\Upsilon }}_0={\mathbf{I}}_4/\sqrt{2}$.

The errors reported do not affect the rest of the paper, or the conclusions.