Connection between the NOON state and a superposition of SU(2) coherent states

The NOON 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. Here we show explicitly the derivation of the NOON state from the superposition state. This derivation makes clear the connection between these seemingly disparate states and shows how the NOON state can be generalized to a superposition of SU(2) coherent states.