The N00N state, which was introduced as a resource for quantum-enhanced metrology, is in fact a special case of a superposition of two SU(2) coherent states. We show here explicitly the derivation of the N00N state from the superposition state. This
derivation makes clear the connection between these seemingly disparate states as well as shows how the N00N state can be generalized to a superposition of SU(2) coherent states.
There has been much recent interest in quantum metrology for applications to sub-Raleigh ranging and remote sensing such as in quantum radar. For quantum radar, atmospheric absorption and diffraction rapidly degrades any actively transmitted quantum
states of light, such as N00N states, so that for this high-loss regime the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the linear Beers law for classical radar attenuation, and which provide sensitivity at the shot-noise limit in the returned power. We show that coherent radar radiation sources, coupled with a quantum homodyne detection scheme, provide both longitudinal and angular super-resolution much below the Rayleigh diffraction limit, with sensitivity at shot-noise in terms of the detected photon power. Our approach provides a template for the development of a complete super-resolving quantum radar system with currently available technology.
