photons - Difference between unpolarized beam and half H+V polarized beam

Let's say that we have got two light beams. Beam A is not polarized at all. Beam B is composed of half H polarized photons + half V polarized photons.

Is there any way to measure those two beams in order to distinguish one from the other ?

The same question applies for a single photon : Is it possible to distinguish a unpolarized single photon from a H or V polarized photon ?

Thanks a lot for your answers !