  Quantum approaches relying on entangled photons have been recently proposed
to increase the efficiency of optical measurements. We demonstrate here that,
surprisingly, the use of classical light with entangled degrees of freedom can
also bring outstanding advantages over conventional measurements in
polarization metrology. Specifically, we show that radially polarized beams of
light allow to perform real-time single-shot Mueller matrix polarimetry. Our
results also indicate that quantum optical procedures requiring entanglement
without nonlocality can be actually achieved in classical optics regime.
