Experimental demonstration of phase measurement precision beating standard quantum limit by projection measurement

We propose and demonstrate experimentally a projection scheme to measure the quantum phase with a precision beating the standard quantum limit. The initial input state is a twin Fock state | N , N ⟩ proposed by Holland and Burnett ( Phys. Rev. Lett. , 71 (1993) 1355) but the phase information is extracted by a quantum state projection measurement. The phase precision is about 1.4/ N for large photon number N , which approaches the Heisenberg limit of 1/ N . Experimentally, we employ a four-photon state from type-II parametric down-conversion and achieve a phase uncertainty of 0.291±0.001 beating the standard quantum limit of for four photons.