A proposed phase-estimation protocol based on measuring the parity of a two-mode squeezed vacuum state at the output of a Mach-Zehnder interferometer shows that the Cramer-Rao sensitivity is sub-Heisenberg [Phys. Rev. Lett. 104, 103602 (2010)]. However, these measurements are problematic, making it unclear if this sensitivity can be obtained with a finite number of measurements. This sensitivity is only for phase near zero, and in this region there is a problem with ambiguity because measurements cannot distinguish the sign of the phase. Here, we consider a finite number of parity measurements, and show that an adaptive technique gives a highly accurate phase estimate regardless of the phase. We show that the Heisenberg limit is reachable, where the number of trials needed for a mean photon number of 1 is approximately 100. We show that the Cramer-Rao sensitivity can be achieved approximately, and the estimation is unambiguous in the interval (-pi/2, pi/2).
Z. Huang, K.R. Motes, P.M. Anisimov, J.P. Dowling, D.W. Berry, Physical Review A 95 (5), 053837