ON THE PHASE SENSITIVITY OF TWO PATH INTERFEROMETRY USING PATH-SYMMETRIC N-PHOTON STATES

It is well known that the estimation of a small phase shift phi from the associated changes in the photon distribution in the output of a two-path interferometer can maximally achieve a sensitivity 1/delta phi equal to the uncertainty Delta(n(1) - n(2)) of the photon number difference between the two paths. In the following, it is shown that the condition for achieving this quantum Cramer-Rao bound at any phase shift Phi(0) is that the state is symmetric with respect to an (unphysical) exchange of the two paths in the interferometer. If this condition is met, the phase sensitivity should be independent of the initial phase shift Phi(0), implying that experimentally observed phase dependences of sensitivity indicate either a non-optimal estimation strategy, or an effect of decoherence.