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arXiv:2603.18807

Time-Multiplexed Distributed Quantum Sensing

Hanbom Yoo, Hyukgun Kwon, Seongjin Hong

quant-phSubmitted Mar 19, 2026• Announced Mar 20, 2026• 0 citations
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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 $Δ^2 φ\propto 1/(NMR)^2$. 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.

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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/N21/N^21/N2 to 1/(NM)21/(NM)^21/(NM)2 through entanglement across both particles and spatial modes, where NNN denotes the photon number and MMM the number of spatially distributed modes. However, the overall sensitivity has remained limited to linear scaling with the number of measurement repetitions RRR. Here, we show that exploiting entanglement across temporal modes via time-domain multiplexing enables a scaling advantage with respect to RRR. As a result, the sensitivity can asymptotically approach simultaneous Heisenberg scaling in photons, spatial modes, and repetitions, yielding an overall sensitivity approaching Δ2φ∝1/(NMR)2Δ^2 φ\propto 1/(NMR)^2Δ2φ∝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.
Distributed quantum metrology has drawn intense interest as it outperforms the optimal classical counterparts in estimating multiple distributed parameters. However, most schemes so far have required entangled resources consisting of photon numbers equal to or more than the parameter numbers, which is a fairly demanding requirement as the number of nodes increases. Here, we present a distributed quantum sensing scenario in which quantum-enhanced sensitivity can be achieved with fewer photons than the number of parameters. As an experimental demonstration, using a two-photon entangled state, we estimate four phases distributed 3 km away from the central node, resulting in a 2.2 dB sensitivity enhancement from the standard quantum limit. Our results show that the Heisenberg scaling can be achieved even when using fewer photons than the number of parameters. We believe our scheme will open a pathway to perform large-scale distributed quantum sensing with currently available entangled sources.
Quantum sensing and quantum metrology propose schemes for the estimation of physical properties, such as lengths, time intervals, and temperatures, achieving enhanced levels of precision beyond the possibilities of classical strategies. However, such an enhanced sensitivity usually comes at a price: the use of probes in highly fragile states, the need to adaptively optimise the estimation schemes to the value of the unknown property we want to estimate, and the limited working range, are some examples of challenges which prevent quantum sensing protocols to be practical for applications. This work reviews two feasible estimation schemes which address these challenges, employing easily realisable resources, i.e., squeezed light, and achieve the desired quantum enhancement of the precision, namely the Heisenberg-scaling sensitivity. In more detail, it is here shown how to overcome, in the estimation of any parameter affecting in a distributed manner multiple components of an arbitrary M-channel linear optical network, the need to iteratively optimise the network. In particular, we show that this is possible with a single-step adaptation of the network based only on a prior knowledge of the parameter achievable through a “classical” shot-noise limited estimation strategy. Furthermore, homodyne measurements with only one detector allow us to achieve Heisenberg-limited estimation of the parameter. We further demonstrate that one can avoid the use of any auxiliary network at the price of simultaneously employing multiple detectors.
Achieving the ultimate quantum precision in the estimation of multiple physical parameters simultaneously is a challenge in quantum metrology due to fundamental limitations and experimental challenges in harnessing the necessary quantum resources. We propose an experimentally feasible scheme to reach Heisenberg-scaling precision in the simultaneous estimation of two unknown phase parameters in a Mach-Zehnder interferometer by using squeezed and coherent states of light as input and homodyne detections at the outputs. Our results open a new research paradigm in harnessing the full quantum advantage of multiparameter estimation in distributed quantum sensing and quantum information processing, as enabled by multiphoton quantum interference with scalable experimental resources.
Distributed quantum sensing, which estimates a global parameter across distant nodes, has attracted significant interest for applications such as quantum imaging, sensor networks, and global-scale clock synchronization. N00N states are regarded as one of the optimal quantum resources for quantum metrology, enabling the Heisenberg scaling. Recently, the concept of N00N states has been extended to multimode N00N states for quantum-enhanced multiple-parameter estimation. However, the application of multimode N00N states in distributed quantum sensing remains unexplored. Here, we propose a distributed quantum sensing scheme that achieves the Heisenberg scaling using multimode N00N states. We theoretically show that multimode N00N states can reach the Heisenberg scaling by examining both the Cramér-Rao bound and the quantum Cramér-Rao bound. For experimental demonstration, we employ a four-mode 2002 state to estimate the average of two spatially distributed phases, achieving a 2.74 dB sensitivity enhancement over the standard quantum limit. We believe that utilizing multimode N00N states for distributed quantum sensing offers a promising approach for developing entanglement-enhanced sensor networks.
Quantum metrology exploits quantum states to achieve an estimation sensitivity beyond classical limits. In the continuous-variable (CV) regime, the squeezed state has been used to implement deterministic quantum sensing, but the quantum metrology sensitivity of this state is significantly affected by losses or detection inefficiencies, which restrict its applications. In this work, quantum distributed sensing is proposed using optical parametric amplified multimode entanglement generated from squeezed states. It is found that the sensitivity is robust to loss or detection inefficiency when large-gain optical parametric amplification (OPA) is introduced, where a two-mode Einstein--Podolsky--Rosen-entangled state and a four-mode cluster state are exploited for analysis. The quantum sensitivity is greatly improved compared to that without OPA in almost all loss scenarios. The quantum Fisher matrix is calculated for both states to obtain the optimal bound in comparison with our scheme, and it is found that even with a small or moderate OPA gain, quantum sensing can be improved compared with the traditional scheme. The states are also compared with corresponding single-mode squeezed states, finding the parameter ranges where entangled states perform better. This study provides a method for realizing large-scale quantum metrology in real-world applications despite losses or detection inefficiencies.
Tracking small transverse displacements of an optical beam with ultra-high accuracy is a fundamental problem underlying numerous important applications ranging from pointing, acquisition and tracking for establishing a lasercom link, to atomic force microscopy for imaging with atomic-scale resolution. Determining what is the optimal quantum-optical probe and the best achievable sensitivity of measuring a small transverse optical beam displacement, is the fundamental question central to these sensing schemes. By mapping this problem to an array of nested Mach-Zehnder interferometers, we explicitly construct the optimal probe state. It is entangled across the spatial modes allowed within the Fresnel number product of the propagation geometry, and entangled across the temporal modes within the time-bandwidth product of the optical probe. We show that the optimal sensitivity of measuring the beam displacement achieves a Heisenberg limited scaling over both the number of temporal modes and the average number of photons transmitted per mode. Surprisingly, we discover a sub-Heisenberg limited scaling over the number of available spatial modes. To qualify the quantum enhancement, we also establish the optimal sensitivity of a classical-light probe, which gives shot-noise limit over both the number of temporal modes and the number of photons per mode, and Heisenberg limited scaling over the number of spatial modes. Finally, we construct an explicit design for quantum-enhanced beam tracking, which uses a Gaussian (multi-mode-entangled squeezed-state) probe and a Gaussian (multi-mode homodyne) receiver.