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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.
When standard light sources are employed, the precision of the phase determination is limited by the shot noise. Quantum entanglement provides means to exceed this limit with the celebrated example of N00N states that saturate the ultimate Heisenberg
Distributed quantum metrology can enhance the sensitivity for sensing spatially distributed parameters beyond the classical limits. Here we demonstrate distributed quantum phase estimation with discrete variables to achieve Heisenberg limit phase mea
By using a systematic optimization approach we determine quantum states of light with definite photon number leading to the best possible precision in optical two mode interferometry. Our treatment takes into account the experimentally relevant situa
A new type of quantum entangled interferometer was recently realized that employs parametric amplifiers as the wave splitting and recombination elements. The quantum entanglement stems from the parametric amplifiers, which produce quantum correlated
The quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters. Similar to the estimation of a constant phase, there is a standard quantum limit for stochastic phase estimation, which can be ob