Parity Measurements in Quantum Optical Metrology

We investigate the utility of parity detection to achieve Heisenberg-limited phase estimation for optical interferometry. We consider the parity detection with several input states that have been shown to exhibit sub shot-noise interferometry with their respective detection schemes. We show that with parity detection, all these states achieve the sub-shot noise limited phase estimate. Thus making the parity detection a unified detection strategy for quantum optical metrology. We also consider quantum states that are a combination of a NOON states and a dual-Fock state, which gives a great deal of freedom in the preparation of the input state, and is found to surpass the shot-noise limit.