Strategies for choosing path-entangled number states for optimal robust quantum optical metrology in the presence of loss

To acquire the best path-entangled photon Fock states for robust quantum optical metrology with parity detection, we calculate phase information from a lossy interferometer by using twin entangled Fock states. We show that (a) when loss is less than 50% twin entangled Fock states with large photon number difference give higher visibility while when loss is higher than 50% the ones with less photon number difference give higher visibility; (b) twin entangled Fock states with large photon number difference give sub-shot-noise limit sensitivity for phase detection in a lossy environment. This result provides a reference on what particular path-entangled Fock states are useful for real world metrology applications.