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To acquire the best path-entangled photon Fock states for robust quantumoptical metrology with parity detection, we calculate phase information from alossy interferometer by using twin entangled Fock states. We show that (a) whenloss is less than 50% twin entangled Fock states with large photon numberdifference give higher visibility while when loss is higher than 50% the oneswith less photon number difference give higher visibility; (b) twin entangledFock states with large photon number difference give sub-shot-noise limitsensitivity for phase detection in a lossy environment. This result provides areference on what particular path-entangled Fock states are useful for realworld metrology applications.

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