  According to quantum theory, two ensembles of quantum systems that are
described by the same density operator are indistinguishable. For example,
unpolarized light can be obtained either by an incoherent mixture of two
orthogonal pure states or by tracing out a photon from a maximally
polarization-entangled photon pair. In both cases, one is unable to guess with
probability greater than 50% the outcome of any polarization measurement, but
the reasons are conceptually different: whereas the first case is a matter of
classical ignorance (the photons were prepared in a definite but unknown way),
the second one is of the quantum ignorance kind - if one cannot access the
other degrees of freedom of the quantum state, there is no information that
could be used to predict a measurement result. We use these concepts to discuss
the quantum-physical interpretation of partially polarized light from the point
of view of quantum communication and whether a polarization scrambler can
really depolarize light. A novel definition of the degree of polarization of a
single photon which does not depend on classical ignorance is also provided.
