Phase estimation with two-mode squeezed-vacuum and parity detection restricted to finite resources

TL;DR

This paper analyzes a phase estimation protocol using two-mode squeezed-vacuum states and parity detection with finite resources, demonstrating near-optimal sensitivity in certain phase regions.

Contribution

It extends previous work by evaluating the finite-resource performance of the protocol using Bayesian analysis, revealing bias issues and conditions for optimal sensitivity.

Findings

Protocol saturates Cramér-Rao bound in certain phase regions

Bias occurs near 0 and π/2 phase values

Scheme beats shot-noise limit with finite resources

Abstract

A recently proposed phase-estimation protocol that is based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that Cram\'{e}r-Rao bound sensitivity can be obtained [P.\ M.\ Anisimov, et al., Phys.\ Rev.\ Lett.\ {\bf104}, 103602 (2010)]. This sensitivity, however, is expected in the case of an infinite number of parity measurements made on an infinite number of photons. Here we consider the case of a finite number of parity measurements and a finite number of photons, implemented with photon-number-resolving detectors. We use Bayesian analysis to characterize the sensitivity of the phase estimation in this scheme. We have found that our phase estimation becomes biased near 0 or $\pi/2$ phase values. Yet there is an in-between region where the bias becomes negligible. In this region, our phase estimation scheme saturates the Cram\'{e}r-Rao bound and beats the shot-noise limit.