Maximum-likelihood analysis of multiple quantum phase measurements

Shapiro, Shepard, and Wong Phys. Rev. Lett. 62, 2377 (1989) suggested that a scheme of multiple phase measurements, using quantum states with minimum ``reciprocal peak likelihood, '' could achieve a phase sensitivity scaling as 1/Nₓ₎ₓ^2, where Nₓ₎ₓ is the mean number of photons availavle for all measurements. We have simulated their scheme for as many as 240 measurements and have found optimum phase sensitivities for 3Nₓ₎ₓ120. A power-law fit to the simulated data yields a phase sensitivity that scales as 1/Nₓ₎ₓ^0. 850. 01. We conclude that reciprocal peak likelihood is not a good measure of sensitivity.