Phase estimation via number-conserving operation inside the SU(1,1) interferometer

TL;DR

This paper proposes a theoretical method to enhance phase measurement precision in SU(1,1) interferometers by implementing number-conserving operations, improving robustness against photon losses and outperforming existing schemes.

Contribution

The study introduces a novel scheme using non-Gaussian, number-conserving operations within SU(1,1) interferometers to improve phase sensitivity and loss robustness.

Findings

PS-then-PA scheme shows superior phase sensitivity improvement.

Number-conserving operations increase quantum Fisher information.

Enhanced robustness against internal photon losses.

Abstract

Utilizing nonlinear elements, SU(1,1) interferometers demonstrate superior phase sensitivity compared to passive interferometers. However, the precision is significantly impacted by photon losses, particularly internal losses. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing number-conserving operations (PA-then-PS and PS-then-PA) within the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We analyze the effects of number-conserving operations on the phase sensitivity, the quantum Fisher information, and the quantum Cramer-Rao bound under both ideal and photon losses scenarios. Our findings reveal that the internal non-Gaussian operations can enhance the phase sensitivity and the quantum Fisher information, and effectively improve the robustness of the SU(1,1) interferometer against internal photon losses. Notably, the PS-then-PA scheme exhibits superior improvement in both ideal and photon losses cases in terms of phase sensitivity. Moreover, in the ideal case, PA-then-PS scheme slightly outperforms PS-then-PA scheme in terms of the quantum Fisher information and the Quantum Cramer-Rao. However, in the presence of photon losses, PS-then-PA scheme demonstrates a greater advantage.