Quantum radar with unreflected photons

Two descriptions are introduced and analyzed for a reflectivity estimation and detection scheme that does not involve measurement of photons scattered by the target. One description, provided by the Hamiltonian dynamics of the full transmitter/receiver optical system, incurs an exponential cost in transmitter intensity for a given estimation sensitivity but is linearly improved with the intensity of the thermal background. The other description, based on optical quantum circuits, exhibits sensitivity around a factor of 1/2 of the optimal entanglement-assisted scheme, but incurs an inverse linear reduction in sensitivity with increasing thermal background. The results have applications for the design of optically active receivers based on combining echo-seeded spontaneous parametric downconversion and induced coherence due to photon indistinguishability.