Parity Measurement is Sufficient for Phase Estimation at the Quantum   Cramer-Rao Bound for Path-Symmetric States
  In this letter, we show that for all the so-called path-symmetric states, the measurement of parity of photon number at the output of an optical interferometer achieves maximal phase sensitivity at the quantum Cramer-Rao bound. Such optimal phase sensitivity with parity is attained at a suitable bias phase, which can be determined a priori. Our scheme is applicable for local phase estimation. 
Sejong Kim, Kaushik P. Seshadreesan, Jonathan P. Dowling, and Hwang   Lee
quant-ph