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Exponential advantage in quantum sensing of correlated parameters

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Researchers demonstrated that entangled quantum sensors can achieve exponential advantages over classical sensors when detecting correlated stochastic parameters, surpassing the typical quadratic speedup seen in deterministic parameter estimation. The study presents three key examples: a two-parameter classification task with low-shot advantages, an N-parameter estimation task where entanglement reduces required samples from exponential (2^N) to constant, and magnetization classification in spin chains. A theoretical framework quantifies entanglement’s advantage for specific sensing protocols and parameter distributions, providing a tool to assess performance gains in stochastic environments. Unlike traditional quantum sensing that assumes fixed parameters, this work focuses on fluctuating parameters drawn from correlated distributions, where entanglement exploits classical correlations for superior accuracy. The findings suggest quantum sensors could revolutionize fields like noise detection and thermal system analysis, where stochastic correlations are inherent but difficult to measure classically.

Exponential advantage in quantum sensing of correlated parameters

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AbstractConventionally in quantum sensing, the goal is to estimate one or more unknown parameters that are assumed to be deterministic – that is, they do not change between shots of the quantum-sensing protocol. We instead consider the setting where the parameters are stochastic: each shot of the quantum-sensing protocol senses parameter values that come from independent random draws. In this work, we explore three examples where the stochastic parameters are correlated and show how using entanglement provides a benefit in classification or estimation tasks: (1) a two-parameter classification task, for which there is an advantage in the low-shot regime; (2) an $N$-parameter estimation task and a classification variant of it, for which an entangled sensor requires just a constant number (independent of $N$) shots to achieve the same accuracy as an unentangled sensor using exponentially many (${\sim}2^N$) shots; (3) classifying the magnetization of a spin chain in thermal equilibrium, where the individual spins fluctuate but the total spin in one direction is conserved – this gives a practical setting in which stochastic parameters are correlated in a way that an entangled sensor can be designed to exploit. We also present a theoretical framework for assessing, for a given choice of entangled sensing protocol and distributions to discriminate between, how much advantage the entangled sensor would have over an unentangled sensor. Our work motivates the further study of sensing correlated stochastic parameters using entangled quantum sensors – and since classical sensors by definition cannot be entangled, our work shows the possibility for entangled quantum sensors to achieve an exponential advantage in sample complexity over classical sensors, in contrast to the typical quadratic advantage.Featured image: a) Conventional quantum sensing tasks estimate or classify an (most generally) $N$-dimensional parameter vector $\theta$ using samples obtained from a quantum sensor. For each sample, the same deterministic $\theta$ is received by the quantum sensor. b) In quantum sensing of stochastic parameters, which we consider in this work, the $N$-dimensional parameter vector $\theta$ received by the quantum sensor is sampled from a probability distribution $\mathcal{P}_{\Phi}(\theta)$. Each sample obtained from the quantum sensor experiences a different, stochastic $\theta$. Estimates made using quantum sensor measurement outcomes in this setting consequently depend on the properties of the underlying distribution $\mathcal{P}_{\Phi}(\theta)$. In this work, we show the advantages of entanglement in the quantum sensor in this latter setting.Popular summaryQuantum sensors can reach the Heisenberg limit in estimating unknown static parameters, where the error scales as $\tfrac{1}{N}$ for an entangled sensor of N qubits. This provides an advantage over classical sensors, which can reach the standard quantum limit, where the error scales as $\tfrac{1}{\sqrt{{N}}}$. In this setting of estimating parameters that are unknown but deterministic, entanglement enables a polynomial advantage in the samples needed to achieve a given error. We consider the setting where the parameters to be sensed are stochastic: they randomly change between each run of the sensing protocol. We show how entanglement can sometimes provide a much larger — even exponential — advantage in samples when the parameters are classically correlated.► BibTeX data@article{Prabhu2026exponential, doi = {10.22331/q-2026-01-14-1963}, url = {https://doi.org/10.22331/q-2026-01-14-1963}, title = {Exponential advantage in quantum sensing of correlated parameters}, author = {Prabhu, Sridhar and Kremenetski, Vladimir and Khan, Saeed A. and Yanagimoto, Ryotatsu and McMahon, Peter L.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {1963}, month = jan, year = {2026} }► References [1] C. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing. Reviews of Modern Physics 89, 035002 (2017). https://doi.org/10.1103/RevModPhys.89.035002 [2] V. Giovannetti, S. Lloyd, and L. Maccone, Quantum Metrology.

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The American Mathematical Monthly 62, 26–29 (1955). https://doi.org/10.2307/2308012Cited byCould not fetch Crossref cited-by data during last attempt 2026-01-14 11:06:49: Could not fetch cited-by data for 10.22331/q-2026-01-14-1963 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-01-14 11:06:49: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractConventionally in quantum sensing, the goal is to estimate one or more unknown parameters that are assumed to be deterministic – that is, they do not change between shots of the quantum-sensing protocol. We instead consider the setting where the parameters are stochastic: each shot of the quantum-sensing protocol senses parameter values that come from independent random draws. In this work, we explore three examples where the stochastic parameters are correlated and show how using entanglement provides a benefit in classification or estimation tasks: (1) a two-parameter classification task, for which there is an advantage in the low-shot regime; (2) an $N$-parameter estimation task and a classification variant of it, for which an entangled sensor requires just a constant number (independent of $N$) shots to achieve the same accuracy as an unentangled sensor using exponentially many (${\sim}2^N$) shots; (3) classifying the magnetization of a spin chain in thermal equilibrium, where the individual spins fluctuate but the total spin in one direction is conserved – this gives a practical setting in which stochastic parameters are correlated in a way that an entangled sensor can be designed to exploit. We also present a theoretical framework for assessing, for a given choice of entangled sensing protocol and distributions to discriminate between, how much advantage the entangled sensor would have over an unentangled sensor. Our work motivates the further study of sensing correlated stochastic parameters using entangled quantum sensors – and since classical sensors by definition cannot be entangled, our work shows the possibility for entangled quantum sensors to achieve an exponential advantage in sample complexity over classical sensors, in contrast to the typical quadratic advantage.Featured image: a) Conventional quantum sensing tasks estimate or classify an (most generally) $N$-dimensional parameter vector $\theta$ using samples obtained from a quantum sensor. For each sample, the same deterministic $\theta$ is received by the quantum sensor. b) In quantum sensing of stochastic parameters, which we consider in this work, the $N$-dimensional parameter vector $\theta$ received by the quantum sensor is sampled from a probability distribution $\mathcal{P}_{\Phi}(\theta)$. Each sample obtained from the quantum sensor experiences a different, stochastic $\theta$. Estimates made using quantum sensor measurement outcomes in this setting consequently depend on the properties of the underlying distribution $\mathcal{P}_{\Phi}(\theta)$. In this work, we show the advantages of entanglement in the quantum sensor in this latter setting.Popular summaryQuantum sensors can reach the Heisenberg limit in estimating unknown static parameters, where the error scales as $\tfrac{1}{N}$ for an entangled sensor of N qubits. This provides an advantage over classical sensors, which can reach the standard quantum limit, where the error scales as $\tfrac{1}{\sqrt{{N}}}$. In this setting of estimating parameters that are unknown but deterministic, entanglement enables a polynomial advantage in the samples needed to achieve a given error. We consider the setting where the parameters to be sensed are stochastic: they randomly change between each run of the sensing protocol. We show how entanglement can sometimes provide a much larger — even exponential — advantage in samples when the parameters are classically correlated.► BibTeX data@article{Prabhu2026exponential, doi = {10.22331/q-2026-01-14-1963}, url = {https://doi.org/10.22331/q-2026-01-14-1963}, title = {Exponential advantage in quantum sensing of correlated parameters}, author = {Prabhu, Sridhar and Kremenetski, Vladimir and Khan, Saeed A. and Yanagimoto, Ryotatsu and McMahon, Peter L.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {1963}, month = jan, year = {2026} }► References [1] C. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing. Reviews of Modern Physics 89, 035002 (2017). https://doi.org/10.1103/RevModPhys.89.035002 [2] V. Giovannetti, S. Lloyd, and L. Maccone, Quantum Metrology.

Physical Review Applied 24, 044055 (2025). https://doi.org/10.1103/6yzb-43rs [15] M. Tsang, H. M. Wiseman, and C. M. Caves, Fundamental quantum limit to waveform estimation.

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Exponential advantage in quantum sensing of correlated parameters

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