Quantum enhanced multiparameter sensing is receiving great attention for its applications to vector sensing, imaging, sensor arrays, and clock networks. While for single parameter sensing, a clear theoretical framework has been developed, multiparameter sensing is surprisingly complex from a conceptual point of view. In this talk I will present our proof-of-principle experiment in multiparameter quantum enhanced sensing with a spatially separated array of entangled 87Rb atomic sensors. The production of these entangled sensors and flexible manipulation of the entanglement to optimize the sensor’s sensitivity will be described. Some of the conceptual questions regarding multiparameter sensing will also be addressed.
Quantum enhanced multiparameter sensing is receiving great attention for its applications to vector sensing, imaging, sensor arrays, and clock networks. While for single parameter sensing, a clear theoretical framework has been developed, multiparameter sensing is surprisingly complex from a conceptual point of view. In this talk I will present our proof-of-principle experiment in multiparameter quantum enhanced sensing with a spatially separated array of entangled 87Rb atomic sensors. The production of these entangled sensors and flexible manipulation of the entanglement to optimize the sensor’s sensitivity will be described. Some of the conceptual questions regarding multiparameter sensing will also be addressed.
In quantum metrology, entangled states of many-particle systems are investigated to enhance measurement precision of the most precise clocks and field sensors. Whereas single-parameter quantum metrology is well established, joint multiparameter estimation poses conceptual challenges and has been explored only theoretically. We experimentally demonstrated multiparameter quantum metrology with an array of entangled atomic ensembles. By splitting a spin-squeezed ensemble, we created an atomic sensor array featuring intersensor entanglement that can be flexibly configured to enhance measurement precision of multiple parameters jointly. Using an optimal estimation protocol, we achieved substantial gains over the standard quantum limit in key multiparameter estimation tasks, thus grounding the concept of quantum enhancement of field sensor arrays and imaging devices.
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 m-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 nonlocal correlations that exist in quantum physics can be used in a sensor network to improve the sensitivity of the measurement of an extended field or some of its spatial features. Taking an atomic ensemble in a spin squeezed state distributed in different spatial modes (the sensors) as a resource, I will show what kind of gain can be obtained in two different cases. First, assuming that local manipulations can be made on the sensors but all measurements are collective [1], and second, including some experimental results [2], assuming that both local manipulations and local measurements are possible on each sensor. Generalising to the case of a large number of sensors, we show applications to imaging and compressed sensing. --- References : [1] "Quantum-enhanced multiparameter estimation and compressed sensing of a field" Y. Baamara, M. Gessner, A. Sinatra, SciPost Physics 14, 050 (2023) https://scipost.org/SciPostPhys.14.3.050 ; [2] "Multiparameter estimation with an array of entangled atomic sensors" Yifan Li, Lex Joosten, Youcef Baamara, Paolo Colciaghi, Alice Sinatra, Philipp Treutlein, Tilman Zibold, https://arxiv.org/abs/2504.08677.
Recent years have witnessed a growing interest in understating the limitations imposed by quantum noise in precision measurements and devising techniques to reduce it. The attention is currently turning to the simultaneously estimation of several parameters of interest, driven by its promising potential across a wide range of sensing applications as well as fueled by experimental progress in various optical and atomic platforms. Here, we provide a comprehensive overview of key research directions in multiparameter quantum sensing and metrology, highlighting both opportunities and challenges. We introduce the basic framework, discuss ultimate sensitivity bounds, optimal measurement strategies, and the role of quantum incompatibility, showing important differences with respect to single-parameter estimation. Additionally, we discuss emerging experimental implementations in distributed quantum sensing, including cutting-edge optimization techniques. This review aims to bridge the gap between theory and experiments, paving the way for the next-generation of quantum sensors and their integration with other quantum technologies.
We introduce a general model for a network of quantum sensors, and we use this model to consider the following question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or nonlinear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.
Conventional multiparameter quantum sensing relies on joint estimation, but this approach faces two key limitations: theoretical bounds may be unattainable due to measurement incompatibility, and sensing may fail due to parameter interdependencies. We propose stepwise estimation and identify regimes where it outperforms joint estimation. For multiple quantum sensors, this scheme achieves far lower error bounds than joint estimation. With many-body probes, stepwise sensing retains a quantum-enhanced scaling advantage often lost in joint estimation due to parameter correlations. We demonstrate its concrete advantages through Bayesian implementations across diverse examples.