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In this letter, we show that for all the so-called path-symmetric states, themeasurement of parity of photon number at the output of an opticalinterferometer achieves maximal phase sensitivity at the quantum Cramer-Raobound. Such optimal phase sensitivity with parity is attained at a suitablebias phase, which can be determined a priori. Our scheme is applicable forlocal phase estimation.

Parity Measurement is Sufficient for Phase Estimation at the Quantum Cramer-Rao Bound for Path-Symmetric States