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arXiv:2512.15876

On the power of moving quantum sensors: fully flexible and noise-resilient sensing

Paul Aigner, Wolfgang Dür

quant-phSubmitted Dec 17, 2025• Announced Dec 19, 2025• 0 citations
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Abstract

We show that a single moving quantum sensor provides complete access to spatially correlated scalar fields. We demonstrate that with either trajectory or internal state control, one can selectively measure any linear functional, e.g. a gradient or a spatial Fourier series coefficient, while successfully eliminating {\it all} noise signals with orthogonal spatial correlation. This even exceeds the capabilities of a sensor network consisting of multiple entangled, yet spatially fixed, quantum sensors, where the number of suppressed noise signals is limited by the number of sensor positions. We show that one can achieve an improved scaling of the quantum Fisher information for moving sensors beyond the static fundamental limit of $T^2$.

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We show that a single moving quantum sensor provides complete access to spatially correlated scalar fields. We demonstrate that with either trajectory or internal state control, one can selectively measure any linear functional, e.g. a gradient or a spatial Fourier series coefficient, while successfully eliminating {\it all} noise signals with orthogonal spatial correlation. This even exceeds the capabilities of a sensor network consisting of multiple entangled, yet spatially fixed, quantum sensors, where the number of suppressed noise signals is limited by the number of sensor positions. We show that one can achieve an improved scaling of the quantum Fisher information for moving sensors beyond the static fundamental limit of T2T^2T2.
Noise sensing underlies many physical applications including tests of non-classicality, thermometry, verification of correlated phases of quantum matter, and characterization of criticality. While previous works have shown that quantum resources such as entanglement and squeezing can enhance the sensitivity in estimating deterministic signals, less is known about the entanglement advantage in sensing correlated stochastic signals (noise). In this work, we compute the fundamental sensitivity limits of quantum sensors in probing spatiotemporally correlated noise. We first prove the fundamental quantum limits in sensing spatially correlated Markovian noise using entangled and unentangled sensors, respectively. Focusing on power-law spatial noise correlations, which naturally arise in condensed matter systems with long-range interactions and/or near criticality, we further derive a scalable entanglement advantage when the power-law decays slowly. Then, considering a target signal with a 1/fp1/f^{p}1/fp-type spectrum, we demonstrate that non-Markovianity may entirely modify the nature of entanglement advantage in estimating spatial noise correlations. Our protocols can be implemented using state-of-the-art quantum sensing platforms including solid-state defects, superconducting circuits, and neutral atoms.
Abstract We consider the selective sensing of planar waves in the presence of noise. We present different methods to control the sensitivity of a quantum sensor network, which allow one to decouple it from arbitrarily selected waves while retaining sensitivity to the signal. Comparing these methods with classical (non-entangled) sensor networks we demonstrate two advantages. First, entanglement increases precision by enabling the Heisenberg scaling. Second, entanglement enables the elimination of correlated noise processes corresponding to waves with different propagation directions, by exploiting decoherence-free subspaces. We then provide a theoretical and numerical analysis of the advantage offered by entangled quantum sensor networks, which is not specific to waves and can be of general interest. We demonstrate an exponential advantage in the regime where the number of sensor locations is comparable to the number of noise sources. Finally, we outline a generalization to other waveforms, e.g. spherical harmonics and general time-dependent fields.
Quantum sensor networks promise precision advantages over classical and single-sensor strategies, in particular when the estimator is non-local. We address the problem of finding such estimators through a framework we connote spatial quantum sensing: given an underlying field interrogated by a network of quantum sensors at fixed positions, construct an estimator for a property of the field, for example, distinguishing a source of signal, or evaluating the field or its derivatives at an arbitrary point. We first treat polynomial fields, casting the task as an interpolation problem, and then generalize to fields modeled by analytic functions, which yields general least-squares estimators. A central and largely unaddressed question is under what conditions on sensor placement these estimators are well-defined and error-free. For mmm-dimensional arrays we give explicit constructions and proofs in the interpolation setting using algebraic geometry, and establish necessary and sufficient conditions in the general case. Comparing a non-local entangled protocol with the best local strategy, we show that entanglement yields maximal precision in distributed sensing under global resource constraints. Finally, we introduce error-free subspaces, a technique that translates prior knowledge of the field into a reduction in the number of required sensors. We expect these techniques to be broadly useful in sensing problems across scales, ranging from earth-scale experiments to local applications such as biological imaging.
The quantum trajectory sensing problem seeks quantum sensor states which enable the trajectories of incident particles to be distinguished using a single measurement. For an nnn-qubit sensor state to unambiguously discriminate a set of trajectories with a single projective measurement, all post-trajectory output states must be mutually orthogonal; therefore, the 2n2^n2n state coefficients must satisfy a system of constraints which is typically very large. Given that this system is generally challenging to solve directly, we introduce a group-theoretic framework which simplifies the criteria for sensor states and exponentially reduces the number of equations and variables involved when the trajectories obey certain symmetries. These simplified criteria yield general families of trajectory sensor states and provide bounds on the particle-sensor interaction strength required for perfect one-shot trajectory discrimination. Furthermore, we establish a link between trajectory sensing and quantum error correction, recognizing their common motivation to identify perturbations using projective measurements. Our sensor states in fact form novel quantum codes, and conversely, a number of familiar stabilizer codes (such as toric codes) also provide trajectory sensing capabilities. This connection enables noise-resilient trajectory sensing through the concatenation of sensor states with quantum error-correcting codes.
We introduce a general model for a network of quantum sensors, and we use this model to consider the question: when do correlations (quantum or classical) between quantum sensors enhance the precision with which the network can measure an unknown set of parameters? We rigorously answer this question for a range of practically important problems. When each sensor in the network measures a single parameter, we show that correlations between sensors cannot increase the estimation precision beyond what can be achieved with an uncorrelated scheme, regardless of the particular details of the estimation problem in question. We also consider the more general setting whereby each sensor may be used to measure multiple parameters, e.g., the three spatial components of a magnetic field. In this case, we show that correlations between sensors can only provide, at best, a small constant precision enhancement, over uncorrelated estimation techniques. Finally, we consider optimizing the network for measuring a single linear function of the unknown parameters, e.g., the average of all of the parameters. Here quantum correlations between the sensors can provide a significant precision enhancement over uncorrelated techniques, and this enhancement factor scales with the number of sensors. To illustrate the broad implications of this work, we apply our results to a wide range of estimation problems of practical interest, including multi-mode optical interferometry, networks of atomic sensors, and networks of clocks. Our findings shed light on a number of results in the literature, provide a rigorous general framework for future research on networked quantum sensors, and have implications for both quantum multi-parameter estimation theory, and quantum sensing technologies.
The quantum trajectory sensing problem seeks quantum sensor states which enable the trajectories of incident particles to be distinguished using a single measurement. For an nnn-qubit sensor state to unambiguously discriminate a set of trajectories with a single projective measurement, all post-trajectory output states must be mutually orthogonal; therefore, the 2n{2}^{n}2n state coefficients must satisfy a system of constraints which is typically very large. Given that this system is generally challenging to solve directly, we introduce a group-theoretic framework which simplifies the criteria for sensor states and exponentially reduces the number of equations and variables involved when the trajectories obey certain symmetries. These simplified criteria yield general families of trajectory sensor states and provide bounds on the particle-sensor interaction strength required for perfect one-shot trajectory discrimination. Furthermore, we establish a link between trajectory sensing and quantum error correction, recognizing their common motivation to identify perturbations using projective measurements. Our sensor states in fact form quantum codes, and conversely, a number of familiar stabilizer codes (such as toric codes) also provide trajectory sensing capabilities. This connection enables noise-resilient trajectory sensing through the concatenation of sensor states with quantum error-correcting codes.