A Quantum Phase Representation of Heisenberg Limits and a Minimally   Resourced Quantum Phase Estimator
  Within the quantum phase representation we derive Heisenberg limits, in closed form, for N00N states and two other classes of states that can perform better in terms of local performance metrics relevant for multiply-peaked distributions. One of these can also enhance the super-resolution factor beyond that of a N00N state of the same power, at the expense of diminished fringe visibility. An accurate phase estimation algorithm, which can be applied to the minimally resourced apparatus of a standard interferometer, is shown to be resilient to the presence of additive white-Gaussian noise (AWGN). In the limit of no AWGN the algorithm achieves over nine digits of accuracy for the case of a four-photon N00N state - orders of magnitude below its Heisenberg limit. 
Scott Roger Shepard, Frederick Ira Moxley III, Jonathan P. Dowling
quant-ph