Interacting quantum systems are attracting increasing interest for developing precise metrology. In particular, the realisation that quantum-correlated states and the dynamics of interacting systems can lead to entirely new and unexpected phenomena have initiated an intense research effort to explore interaction-based metrology both theoretically and experimentally. However, the current framework of interaction-based metrology mainly focuses on single-parameter estimations, a demonstration of multiparameter metrology using interactions as a resource was heretofore lacking. Here we demonstrate an interaction-based multiparameter metrology with strongly interacting nuclear spins. We show that the interacting spins become intrinsically sensitive to all components of a multidimensional field when their interactions are significantly larger than their Larmor frequencies. Using liquid-state molecules containing strongly interacting nuclear spins, we demonstrate the proof-of-principle estimation of all three components of an unknown magnetic field and inertial rotation. In contrast to existing approaches, the present interaction-based multiparameter sensing does not require external reference fields and opens a path to develop an entirely new class of multiparameter quantum sensors.
Interacting quantum systems are attracting increasing interest for developing precise metrology. In particular, the realisation that quantum-correlated states and the dynamics of interacting systems can lead to entirely new and unexpected phenomena have initiated an intense research effort to explore interaction-based metrology both theoretically and experimentally. However, the current framework of interaction-based metrology mainly focuses on single-parameter estimations, a demonstration of multiparameter metrology using interactions as a resource was heretofore lacking. Here we demonstrate an interaction-based multiparameter metrology with strongly interacting nuclear spins. We show that the interacting spins become intrinsically sensitive to all components of a multidimensional field when their interactions are significantly larger than their Larmor frequencies. Using liquid-state molecules containing strongly interacting nuclear spins, we demonstrate the proof-of-principle estimation of all three components of an unknown magnetic field and inertial rotation. In contrast to existing approaches, the present interaction-based multiparameter sensing does not require external reference fields and opens a path to develop an entirely new class of multiparameter quantum sensors.
Quantum sensing utilizes the quantum resources of well-controlled quantum systems to measure small signals with high sensitivity, and has great potential in both fundamental science and concrete applications. Interacting quantum systems have attracted increasing interest in the field of precise measurements, owing to their potential to generate quantum-correlated states and exhibit rich many-body dynamics. These features provide a novel avenue for exploiting quantum resources in sensing applications. Although previous studies have shown that using such systems can improve sensitivity, they mainly focused on measuring individual physical quantities. In experiment, the challenge of using interacting quantum systems to achieve high-precision measurements of multiple physical parameters simultaneously has not been explored to a large extent. In this study, we demonstrate a first realisation of interaction-based multiparameter sensing by using strongly interacting nuclear spins under ultra-low magnetic field conditions. We find that, as the interaction strength among nuclear spins becomes significantly larger than their Larmor frequencies, a different regime emerges where the strongly interacting spins can be simultaneously sensitive to all components of a multidimensional field, such as a three-dimensional magnetic field. Moreover, we observe that the strong interactions between nuclear spins can increase their quantum coherence times to as long as several seconds, thereby improving measurement precision. Our sensor successfully achieves precision measurement of three-dimensional vector magnetic fields with a field sensitivity reaching the order of 10–11 T and an angular resolution as high as 0.2 rad. Importantly, this approach eliminates the need for external reference fields, thereby avoiding calibration errors and technical noise commonly encountered in traditional magnetometry. Experimentally optimized protocol further enhances the sensitivity of the interacting spin-based sensor by up to five orders of magnitude compared with non-interacting or classical schemes. These results demonstrate the enormous potential of interacting spin systems as a powerful platform for high-precision multi-parameter quantum sensing. The techniques developed here pave the way for a new generation of quantum sensors that use intrinsic spin interactions to exceed the traditional sensitivity limits, presenting a promising route toward ultra-sensitive, calibration-free magnetometry in complex environments.
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.
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 multiparameter estimation promises to extend quantum advantage to the simultaneous high-precision measurements of multiple physical quantities. However, realizing this capability in practical quantum sensors under realistic conditions remains challenging due to intrinsic system imperfections. Here, we experimentally demonstrate multiparameter estimation using a nitrogen-vacancy (NV) center in diamond, a widely adopted solid-state quantum sensor. Leveraging electronic-nuclear spin entanglement and optimized Bell-state measurement at room temperature, we simultaneously estimate the amplitude, detuning, and phase of a microwave drive from a single measurement sequence. Despite practical constraints, our results achieve linear sensitivity scaling for all parameters with respect to interrogation time. This work bridges the gap between foundational quantum estimation theory and real-world quantum sensing, opening pathways toward enhanced multiparameter quantum sensors suitable for diverse scientific and technological applications.
Critical quantum metrology relies on the extreme sensitivity of a system's eigenstates near the critical point of a quantum phase transition to Hamiltonian perturbations. This means that these eigenstates are extremely sensitive to all the parameters of the Hamiltonian. In realistic settings, there is always some degree of uncertainty in the control parameters used to tune the system to criticality. These uncertainties, while not the target of estimation, can significantly affect the attainable precision, effectively acting as nuisance parameters in the estimation process. Despite being a practically relevant source of noise, their impact on critical metrology has been largely overlooked. In this work we present a general framework that interpolates between single- and multiparameter estimation settings, enabling a systematic analysis of how such uncertainties influence sensitivity. We apply this framework to the paradigmatic transverse field Ising and Lipkin-Meshkov-Glick models, explicitly demonstrating how uncertainty in control parameters affects the metrological performance of critical sensors. For finite-size systems, we identify a fundamental trade-off between robustness to uncertainty and the ability to retain a quantum advantage at the critical point. Our results contribute to a deeper understanding of the practical limitations of critical quantum metrology and provide a route toward its more resilient implementation.
We consider the simultaneous estimation of multiple parameters in Hamiltonians of the form Hθ=HθP+HC, where HθP encodes the unknown parameters and HC is a control term. We consider three basic paradigmatic frameworks for metrology: (i) dynamical, where the parameters are encoded unitarily, (ii) thermal, and (iii) ground state. We generalize previous bounds for single-parameter estimation to simultaneous multiparameter estimation for all three metrological settings and establish the conditions required for their saturability. We then focus on vector magnetometry, deriving tight bounds for the simultaneous estimation of magnetic-field components and identifying optimal many-body control Hamiltonians HC that saturate them. These results establish the fundamental limits of vector magnetometry for unitary dynamics, thermal equilibrium states, and ground states.