Quantum Sensing with Bright Two-Mode Squeezed Light in a Distributed Network of Gyroscopes

TL;DR

This work addresses quantum-enhanced distributed sensing for angular-velocity estimation using bright two-mode squeezed light across a network of optical gyroscopes. It analyzes two probe configurations—M-mode entangled and M separable bTMSS—probing an average phase across spatially separated gyroscopes via joint quadrature measurements to form a global estimator. The study derives analytical and numerical quantum Cramér-Rao bounds and demonstrates that mode-entangled schemes offer a clear advantage over separable ones, particularly under moderate losses, with performance improving as the number of gyroscopes grows. The results indicate a viable path to quantum-enhanced inertial navigation in distributed quantum networks, achievable with realistic squeezing levels and loss tolerance.

Abstract

Recent developments in quantum technologies have enabled significant improvements in the precision of optical sensing systems. This work explores the integration of distributed quantum sensing (DQS) with optical gyroscopes to improve the estimation accuracy of angular velocity. Utilizing bright two-mode squeezed states (bTMSS), which offer high photon numbers and strong bipartite quantum correlations, we propose a novel configuration that leverages continuous-variable entanglement across multiple spatially separated optical gyroscopes. Unlike traditional quantum sensing that enhances a single sensor, our approach focuses on estimating a global phase shift corresponding to the average angular rotation across distributed optical gyroscopes with quantum-enhanced sensitivity. We analyze the phase sensitivities of different bTMSS configurations, including M mode-entangled bTMSS and separable M-bTMSS, and evaluate their performance through the quantum Cramér-Rao bound. The analysis shows that, with 5% photon loss in every channel in the system, the proposed scheme shows a sensitivity enhancement of ~9.3 dB beyond the shot-noise limit, with an initial squeezing of ~9.8 dB. The present scheme has potential applications in quantum-enhanced inertial navigation and precision metrology within emerging quantum networks.

Figures (10)

• Figure 1: Optical gyroscope based on Sagnac interferometer with a 50:50 beam splitter (BS), rotating with an angular velocity of $\Omega$.
• Figure 2: Distributed optical gyroscope configuration with mode-entangled probe states. The parametric amplifier with a squeezing parameter $r$ produces bright two-mode squeezed states in modes $\hat{a}_s$ and $\hat{b}_s$, which are given as inputs to two symmetric beamsplitter networks together with vacuum states in the remaining ports, producing M-mode entangled states at each SBN. They are further directed towards the optical gyroscopes via beam isolators. The beam isolators are beam routing optics (e.g., polarizing beamsplitters with appropriate waveplates) that isolate the input and output modes of the gyroscopes. Later, the phase-shifted output modes of the gyroscopes reach the detectors via the beam isolators, where a joint quadrature measurement is carried out.
• Figure 3: Optimal values of (a) squeezing parameter, $r$, and (b) coherent seed amplitude, $\alpha$, as a function of average photon number, $N$ and number of gyroscope units, $M$, at a given value of transmissivity, $\eta=0.9$.
• Figure 4: Optimized Phase sensitivity $\Delta\phi_e^2$ of the mode-entangled configuration as a function of (a) the number of sensors $M$, at a constant value of average photon number per sensor $N=10$; (b) average photon number per sensor $N$, at a fixed number of sensors $M=4$. In both (a) and (b), the purple dashed trace represents the SNL of the phase sensitivity. The blue solid trace, the orange dashed trace, the green dotted trace, and the red dotted-dash trace represent the phase sensitivity corresponding to $\eta=1.0$, $\eta=0.9$, $\eta=0.5$, and $\eta=0.1$, respectively.
• Figure 5: Distributed optical gyroscope configuration with $M$ separate bTMSS as input states. The M parametric amplifiers, each with the same squeezing parameter $r$, produce bright two-mode squeezed states in modes $a_j$ and $b_j$ ($1 \le j \le M$), which are given as inputs to separate M optical gyroscopes. The phase-shifted modes reach the detectors via the beam isolators, where a joint quadrature measurement is carried out.