  We show that the quantum angle measurement for x-polarized photon number
states results in an angle which will never correspond to the y-axis for an odd
number of photons; yet for an even number of photons it always can. The analogy
of this surprising effect for other particles or ions (qubits in their spin up
state) is presented and we show why such an effect cannot be observed in a
standard SU(2) interferometer. The quantum phase representation of such an
interferometer provides clues as to how its apparatus might be modified in
order to demonstrate these phenomena. The same representation is then used to
provide insight on the range and sensitivity that one can expect from quantum
phase statistical inference algorithms which can surpass the Heisenberg limit.
