Adaptive phase estimation with two-mode squeezed-vacuum and parity measurement

TL;DR

This paper presents an adaptive phase estimation protocol using two-mode squeezed-vacuum states and parity measurements, achieving Heisenberg-limited sensitivity with a finite number of measurements and resolving phase ambiguity.

Contribution

It introduces an adaptive measurement technique that enables Heisenberg-limited phase estimation with two-mode squeezed-vacuum states, overcoming previous measurement limitations.

Findings

Heisenberg limit is achievable with about 100 trials for mean photon number 1.

Adaptive measurements provide unambiguous phase estimates in the interval (-π/2, π/2).

Cramér-Rao sensitivity is approximately attained with finite measurements.

Abstract

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 $\bar{n}=1$ 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 ($-\pi/2, \pi/2$).