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 Cram\'{e}r-Rao sensitivity is sub-Heisenberg [Phys.\ Rev.\ Lett.\ {\bf104}, 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 mean photon number nˉ=1 is approximately one hundred. We show that the Cram\'{e}r-Rao sensitivity can be achieved approximately, and the estimation is unambiguous in the interval (−π/2,π/2).
@article{arxiv.1609.04689,
title = {Adaptive phase estimation with two-mode squeezed-vacuum and parity measurement},
author = {Zixin Huang and Keith R. Motes and Petr M. Anisimov and Jonathan P. Dowling and Dominic W. Berry},
journal= {arXiv preprint arXiv:1609.04689},
year = {2017}
}