MAXIMUM-LIKELIHOOD STATISTICS 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/N(tot)2, where N(tot) is the mean number of photons available for all measurements. We have simulated their scheme for as many as 240 measurements and have found optimum phase sensitivities for 3 less-than-or-equal-to N(tot) less-than-or-equal-to 120; a power-law fit to the simulated data yields a phase sensitivity that scales as 1/N(tot)82+/-0.01. By using a combination of numerical and analytical techniques, we extend our results to higher values of N(tot) than are accessible to our simulations; we find no evidence for phase sensitivities better than the benchmark 1/N(tot) sensitivity of squeezed-state interferometry. We conclude that reciprocal peak likelihood is not a good measure of phase sensitivity. We discuss other factors that are important to phase sensitivity.