Effects of Phase Fluctuations on Phase Sensitivity and Visibility of Path-Entangled Photon Fock States

We study effects of phase fluctuations on phase sensitivity and visibility of a class of robust path-entangled photon Fock states (known as mm’ states) as compared to the maximally path-entangled N00N states in presence of realistic phase fluctuations such as turbulence noise. Our results demonstrate that the mm’ states, which are more robust than the N00N state against photon loss, perform equally well when subject to such fluctuations. We show that the phase sensitivity with parity detection for both of the above states saturates the quantum Cramer-Rao bound in presence of such noise, suggesting that the parity detection presents an optimal detection strategy.