Page "Density matrix" Paragraph 14

Therefore, unpolarized light cannot be described by any pure state, but can be described as a statistical ensemble of pure states in at least two ways ( the ensemble of half left and half right circularly polarized, or the ensemble of half vertically and half horizontally linearly polarized ).

These two ensembles are completely indistinguishable experimentally, and therefore they are considered the same mixed state.

One of the advantages of the density matrix is that there is just one density matrix for each mixed state, whereas there are many statistical ensembles of pure states for each mixed state.

Nevertheless, the density matrix contains all the information necessary to calculate any measurable property of the mixed state.