  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.
