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arXiv:2609.38678

Exponential separation in sensing continuous signals via squeezing

Francesco Anna Mele, Nadine Meister, Haimeng Zhao, Senrui Chen, Hsin-Yuan Huang

quant-phSubmitted Sep 30, 2026• Announced Oct 1, 2026• 0 citations
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Abstract

Quantum sensing traditionally focuses on using quantum resources such as squeezing and entanglement to improve precision for sensing fixed signals. However, in many applications such as gravitational-wave detection and electromagnetic-field sensing, the signal evolves continuously and varies through time. Additionally, the learner is free to prepare, control, and measure the sensor at arbitrary times, possibly chosen adaptively. In this work, we establish exponential separation in sensing time for continuously evolving signals due to the available squeezing. The signals we study are characterized by a pattern size $T$, and we find that a sensor with squeezing at least $ω(\sqrt{\log T})$ offers a $\mathrm{poly}(T)$ sensing time, whereas those with squeezing at most $o(\sqrt{\log T})$ must use an exponential sensing time in $T$.

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124 pages, 12 figures

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Sensing time-varying signals is essential for precision measurement and for characterizing fluctuations in physical systems. In this work, we show that quantum entanglement provides an exponential advantage in the acquisition time required to learn the temporal statistics of a stationary classical signal. The task is to estimate the characteristic function of joint displacements on selected bosonic modes within a fixed-duration window, using continuous measurements of one signal realization. We present an entanglement-assisted scheme based on two-mode squeezed probes and local Bell measurements with protected idlers, and bound its acquisition time accounting for readout noise and correlations between signal windows. For a strictly stationary pulse family, it achieves polynomial acquisition time at inverse-polynomial accuracy with logarithmic squeezing and polynomial photon number. On the other hand, we prove that any local idler-free protocols require acquisition time exponential in the number of selected temporal modes per window. This lower bound holds for both sequentially prepared and arbitrarily temporally entangled probes, allowing non-Gaussian inputs and measurements and causal classical feedback, as long as each output is measured destructively within its time bin. These results establish an exponential quantum learning advantage for a single continuously monitored stationary signal, with the sensing cost measured by total acquisition time.
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One of the most promising applications of quantum networks is entanglement-assisted sensing. The field of quantum metrology exploits quantum correlations to improve the precision bound for applications such as precision timekeeping, field sensing, and biological imaging. When measuring multiple spatially distributed parameters, current literature focuses on quantum entanglement in the discrete-variable case and quantum squeezing in the continuous-variable case, distributed amongst all of the sensors in a given network. However, it can be difficult to ensure that all sensors preshare entanglement of sufficiently high fidelity. This work probes the space between fully entangled and fully classical sensing networks by modeling a star network with probabilistic entanglement generation that is attempting to estimate the average of local parameters. The quantum Fisher information is used to determine which protocols best utilize entanglement as a resource for different network conditions. It is shown that without entanglement distillation there is a threshold fidelity below which classical sensing is preferable. For a network with a given number of sensors and links characterized by a certain initial fidelity and probability of success, this work outlines when and how to use entanglement, when to store it, and when it needs to be distilled.