Optimal Quantum Measurements for Phase Estimation

Abstract

Quantum information theory is applied to practical interferometer-based phase measurements to deduce the optimal phase measurement scheme with two optical modes. Optimal phase measurements, given ideal input states, reveal an asymptotic $1/n$ decrease in phase uncertainty $\Delta \theta$ for $n$ the mean photon number of the input state. In contradistinction to previous schemes for realizing the number-phase uncertainty limit, the $1/n$ limit achieved here is independent of the interferometer phase shift; prior information about the expected phase shift is not necessary to attain this limit. These results apply more generally to su(2) and so(3) phase parameter estimation.