Within the quantum phase representation we derive Heisenberg limits, in closed form, for NOON 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 superresolution factor beyond that of a NOON 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 in 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 NOON state, orders of magnitude below its Heisenberg limit.
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