Optimal quantum radar vs. optimal classical radar with full polarization antennas

We compute the optimal quantum radar detection performance relative to the corresponding optimal classical radar detection performance with full polarization antennas. We use the Belavkin-Zakai equation rather than the Schrödinger equation, because the latter does not have an explicit measurement model. Our calculation is consistent with the well known 6 dB quantum advantage at low photon flux per mode assuming no polarization entanglement of photons and no use of fully polarized antennas.