Bayesian quantum radar with full polarization and hyperentanglement of non-Gaussian photons

Abstract

We show that the optimal quantum radar has 12 dB better effective signal-to-noise ratio compared with the corresponding optimal classical radar, assuming full polarization antennas with hyperentanglement of photons at low photon flux per mode. The photon states are non-Gaussian, and we hyperentangle M-tuples of photons rather than the boring old pairs of photons. Full polarization means that the radar transmits two orthogonal polarizations simultaneously and also receives two polarizations simultaneously. We use the Belavkin-Zakai equation rather than the boring old Schrödinger equation, because the latter does not model macroscopic noisy measurements of quantum systems. We also compute the minimum cost for the optimal quantum radar at X-Band, which is 20 orders of magnitude more than for the corresponding optimal classical radar today. With the most optimistic assumptions this cost ratio can be reduced to only 15 orders of magnitude in the future. We speculate that further improvements in quantum radar are possible by exploiting non-Gaussian states of photons, hyperentanglement of more than pairs of photons, more advanced protocols for entanglement beyond the so-called “quantum illumination,” more advanced technology, more clever ideas and new physics yet to be discovered using Bayesian quantum field theory.