Time-Multiplexed Distributed Quantum Sensing

TL;DR

This paper demonstrates that time-multiplexed entanglement in quantum sensing can achieve near-Heisenberg scaling across photons, modes, and repetitions, significantly enhancing measurement sensitivity.

Contribution

It introduces a novel time-domain multiplexing approach that exploits entanglement across temporal modes, enabling superior scaling in quantum metrology beyond previous spatial mode limitations.

Findings

Achieves asymptotic Heisenberg scaling in photons, modes, and repetitions.

Proves protocol optimality within Gaussian states using Bogoliubov transformations.

Shows robustness of the advantage under optical loss and proposes a feasible experimental scheme.

Abstract

Quantum metrology enables parameter estimation beyond classical limits by exploiting nonclassical resources such as squeezing and entanglement. In distributed quantum sensing, Heisenberg scaling has been extended from $1/N^2$ to $1/(NM)^2$ through entanglement across both particles and spatial modes, where $N$ denotes the photon number and $M$ the number of spatially distributed modes. However, the overall sensitivity has remained limited to linear scaling with the number of measurement repetitions $R$. Here, we show that exploiting entanglement across temporal modes via time-domain multiplexing enables a scaling advantage with respect to $R$. As a result, the sensitivity can asymptotically approach simultaneous Heisenberg scaling in photons, spatial modes, and repetitions, yielding an overall sensitivity approaching $\Delta^2 \phi \propto 1/(NMR)^2$. Using the Bogoliubov transformation formalism, we prove the optimality of the protocol within the class of Gaussian states and show that the scaling is realizable via homodyne detection and maximum-likelihood estimation. We further show that the advantage persists under optical loss and propose an experimentally feasible loop-based photonic sensing scheme. Our results open a route to incorporating time-multiplexing techniques into quantum metrology.