Quantum phase estimation with lossy interferometers

R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, I. A. Walmsley

Published 2009-04-02, updated 2009-06-18Version 2

We give a detailed discussion of optimal quantum states for optical two-mode interferometry in the presence of photon losses. We derive analytical formulae for the precision of phase estimation obtainable using quantum states of light with a definite photon number and prove that maximization of the precision is a convex optimization problem. The corresponding optimal precision, i.e. the lowest possible uncertainty, is shown to beat the standard quantum limit thus outperforming classical interferometry. Furthermore, we discuss more general inputs: states with indefinite photon number and states with photons distributed between distinguishable time bins. We prove that neither of these is helpful in improving phase estimation precision.