Quantum phase estimation with lossy interferometers - Demkowicz-Dobrzanski, R; Dorner, U; Smith, B; Lundeen, J; Wasilewski, W; Banaszek, K; Walmsley, I (2009)
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. © 2009 The American Physical Society.