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We propose and demonstrate experimentally a projection scheme to measure thequantum phase with a precision beating the standard quantum limit. The initialinput state is a twin Fock state $|N,N>$ proposed by Holland and Burnett [Phys.Rev. Lett. {\bf 71}, 1355 (1993)] but the phase information is extracted by aquantum state projection measurement. The phase precision is about $1.4/N$ forlarge photon number $N$, which approaches the Heisenberg limit of 1/N.Experimentally, we employ a four-photon state from type-II parametricdown-conversion and achieve a phase uncertainty of $0.291\pm 0.001$ beating thestandard quantum limit of $1/\sqrt{N} = 1/2$ for four photons.

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