Practical resources and measurements for lossy optical quantum metrology

TL;DR

This paper investigates practical quantum resources and measurement schemes for phase estimation in lossy optical interferometers, demonstrating the advantages and robustness of different states and detection methods under realistic conditions.

Contribution

It compares the effectiveness of two practical quantum states and measurement schemes in lossy interferometry, highlighting the robustness of homodyne detection.

Findings

Two-mode squeezed vacuum state outperforms coherent and squeezed states under photon loss.

Homodyne detection is more robust against photon loss than photon number resolving detection.

Double homodyne detection improves phase estimation accuracy in lossy conditions.

Abstract

We study the sensitivity of phase estimation in a lossy Mach-Zehnder interferometer (MZI) using two general, and practical, resources generated by a laser and a nonlinear optical medium with passive optimal elements, which are readily available in the laboratory: One is a two-mode separable coherent and squeezed vacuum state at a beam splitter and the other is a two-mode squeezed vacuum state. In view of the ultimate precision given by quantum Fisher information, we show that the two-mode squeezed vacuum state can achieve a lower bound of estimation error than the coherent and squeezed vacuum state under a photon-loss channel. We further consider practical measurement schemes, homodyne detection and photon number resolving detection (PNRD), to characterize the accuracy of phase estimation in reality and find that the coherent and squeezed vacuum state largely achieves a lower bound than the two-mode squeezed vacuum in the lossy MZI while maintaining quantum enhancement over the shot-noise limit. By comparing homodyne detection and PNRD, we demonstrate that quadrature measurement with homodyne detection is more robust against photon loss than parity measurement with PNRD. We also show that double homodyne detection can provide a better tool for phase estimation than single homodyne detection against photon loss.