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 $\left(\text{a}\right)$ 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; and $\left(\text{b}\right)$ 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.

• Received 28 April 2012

DOI:https://doi.org/10.1103/PhysRevA.86.013826