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Quantum sensor’s ability for multi-parameter estimation in joint quantum thermometry and magnetometry

Seyed Mohammad Hosseiny, Milad Norouzi

Published Oct 3, 2025• 0 citations
Publisher

Abstract

Abstract Quantum sensors can enable the simultaneous and precise measurement of multiple physical parameters, facilitating the development of dual-sensing techniques. In this paper, we report on the simultaneous multi-parameter quantum sensing of temperature and magnetic field based on a quantum sensor consisting of a two-qubit Heisenberg XYZ chain, which enables joint quantum thermometry and magnetometry. Qubits interact via ferromagnetic and antiferromagnetic couplings, and are in thermal equilibrium with a heat bath in the presence of an external magnetic field. Specifically, the sensor’s response to perturbations, like temperature and magnetic field changes, is analyzed through quantum Fisher information (QFI), providing a measure of the sensing precision. We investigate the effects of different types of inter-qubit couplings and external magnetic fields on the accuracy of multi-parameter estimation. Our results demonstrate that simultaneous multi-parameter estimation improves the speed of information extraction and processing, accuracy, and sensitivity of our quantum sensor. This work provides a promising avenue for developing high-performance multiparameter quantum sensors with potential applications in various fields, including materials science, biomedicine, environmental monitoring, aerospace, industrial production, and other fields.

DOI
10.21203/rs.3.rs-7240932/v1

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Abstract Quantum sensors can enable the simultaneous and precise measurement of multiple physical parameters, facilitating the development of dual-sensing techniques. In this paper, we report on the simultaneous multi-parameter quantum sensing of temperature and magnetic field based on a quantum sensor consisting of a two-qubit Heisenberg XYZ chain, which enables joint quantum thermometry and magnetometry. Qubits interact via ferromagnetic and antiferromagnetic couplings, and are in thermal equilibrium with a heat bath in the presence of an external magnetic field. Specifically, the sensor’s response to perturbations, like temperature and magnetic field changes, is analyzed through quantum Fisher information (QFI), providing a measure of the sensing precision. We investigate the effects of different types of inter-qubit couplings and external magnetic fields on the accuracy of multi-parameter estimation. Our results demonstrate that simultaneous multi-parameter estimation improves the speed of information extraction and processing, accuracy, and sensitivity of our quantum sensor. This work provides a promising avenue for developing high-performance multiparameter quantum sensors with potential applications in various fields, including materials science, biomedicine, environmental monitoring, aerospace, industrial production, and other fields.
This study examines a quantum sensor consisting of two qubits modeled in an XXZ Heisenberg spin chain under a homogeneous magnetic field, for use in quantum thermometry and magnetometry. The sensor is subjected to a common classical environment driven by static noise and is in thermal equilibrium with a heat bath. We analyze the impact of spin–spin, Dzyaloshinskii–Moriya, and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions, as well as the static noise characterized by the disorder parameter, on the sensor's time-evolved state. We also assess the influence of magnetic field homogeneity on performance. Employing quantum Fisher information criteria, we determine the sensor's metrological precision. The performance of the proposed sensor in estimating the external magnetic field and temperature in weak and strong field regimes is different over time with temperature variations. In the strong magnetic field regime, static noise reduces the sensitivity of quantum sensing, while in the weak field regime, this effect is negligible. Our sensor achieves optimal sensitivity and precision for temperature and magnetic field estimation in the presence of static noise and in the weak magnetic field and low temperature regime. Finally, we demonstrate that the quantum sensor achieves a stable sensitivity and precision in its performance over time in quantum magnetometry and thermometry, which can be very valuable in quantum sensing. Moreover, we propose some experimental platforms for the realization of our quantum sensor.
ABSTRACT Quantum sensors are devices that utilize quantum systems' properties to achieve high‐precision measurements of physical quantities, such as magnetic fields and temperature. The metrological precision of quantum sensors refers to their ability to provide accurate and reliable measurements with minimal uncertainty. In this paper, we propose a quantum sensor consisting of multiple atoms arranged in a spin chain, exposed to a thermal bath at a temperature and an external weak magnetic field with a magnetic‐field gradient for quantum thermometry and magnetometry. Employing the Hilbert‐Schmidt speed (HSS), a popular measure of quantum statistical speed to quantify precision limits in parameter estimation theory, we have investigated in detail how the magnetic‐field gradient and spin chain position influence the quantum sensor's metrological capabilities. We show that the performance and precision of our quantum sensor depend on the spin chain position and the magnetic field and its gradient; increasing these factors' values reduces estimation precision and weakens quantum sensor performance. Finally, increasing the number of atoms in a quantum sensing structure improves the accuracy of temperature and field estimation.
We investigate multiparameter quantum estimation in a Raman-coupled two-qubit system at thermal equilibrium. Analytical expressions for the quantum Fisher information matrix are derived to characterize the simultaneous estimation of the temperature and Raman coupling strength. The corresponding quantum Cramér--Rao bounds are obtained and compared with those of individual estimation strategies. Our results reveal optimal operating regimes determined by the interplay between thermal fluctuations and coherent interactions. In particular, quantum thermometry exhibits a well-defined optimal temperature window, whereas the estimation of the Raman coupling strength is significantly enhanced in the low-temperature and weak-coupling regime. We further show that simultaneous estimation can outperform independent estimation within appropriate parameter regions, highlighting the advantages of multiparameter quantum metrology. These results provide analytical insights into the ultimate precision limits of Raman-coupled two-qubit systems and identify promising operating regimes for quantum sensing and quantum thermometry.
We study the performance of quantum sensors composed of four qubits arranged in different geometries for magnetometry and thermometry. The qubits interact via the transverse-field Ising model with both ferromagnetic and antiferromagnetic couplings, maintained in thermal equilibrium with a heat bath under an external magnetic field. Using quantum Fisher information, we evaluate the metrological precision of these sensors. For ferromagnetic couplings, weakly connected graphs (e.g., the chain graph, P_4) perform optimally in estimating weak magnetic fields, whereas highly connected graphs (e.g., the complete graph, K_4) excel at strong fields. Conversely, K_4 achieves the highest sensitivity for temperature estimation in the weak-field regime. In the antiferromagnetic case, we uncover a fundamental trade-off dictated by spectral degeneracy: configurations with non-degenerate energy spectra - such as the pan-like graph (three qubits in a triangle with the fourth attached) - exhibit strong magnetic field sensitivity due to their pronounced response to perturbations. In contrast, symmetric structures like the square graph, featuring degenerate energy levels (particularly ground-state degeneracy), are better suited for precise thermometry. Notably, our four-qubit sensors achieve peak precision in the low-temperature, weak-field regime. Finally, we introduce a spectral sensitivity measure that quantifies energy spectrum deformations under small perturbations, providing a simple heuristic indicator of metrological sensitivity.
Quantum thermometry leveraging quantum sensors is investigated with an emphasis on fundamental precision bounds derived from quantum estimation theory. The proposed sensing platform consists of two dissimilar qubits coupled via capacitor, which induce quantum oscillations in the presence of a thermal environment. Thermal equilibrium states are modeled using the Gibbs distribution. The precision limits are assessed through the Quantum Fisher Information (QFI) and the Hilbert-Schmidt Speed (HSS), serving as stringent criteria for sensor sensitivity. Systematic analysis of the dependence of QFI and HSS on tunable parameters -such as qubit energies and coupling strengths- provides optimization pathways for maximizing temperature sensitivity. Furthermore, we explore two distinct quantum thermometry paradigms: (I) local temperature estimation directly performed by Alice, who possesses the quantum sensor interfacing with the thermal bath, and (II) remote temperature estimation conducted by Bob, facilitated via quantum teleportation. In the latter scenario, temperature information encoded in the qubit state is transmitted through a single-qubit quantum thermal teleportation protocol. Our findings indicate that direct measurement yields superior sensitivity compared to remote estimation, primarily due to the inherent advantage of direct sensor-environment interaction. The analysis reveals that increasing Josephson energies diminishes sensor sensitivity, whereas augmenting the mutual coupling strength between the qubits enhances it.
Nanoscale thermometry and magnetometry are in high demand across a wide range of scientific and technological applications. In this context, optically addressable spins in solids have emerged at the forefront of on-chip quantum sensing. However, simultaneous quantum sensing of multiple parameters (e.g., temperature and magnetic field) using the same spin sensor remains challenging due to cross-sensitivity to multiple physical quantities. Here, we demonstrate independent dual sensing of temperature and magnetic field using single quantum emitters in hexagonal boron nitride (hBN). We experimentally verify the independent response of the zero-phonon line (ZPL) position to temperature and of optically detected magnetic resonance (ODMR) to magnetic fields. Furthermore, we demonstrate local temperature sensing of a microcircuit while simultaneously measuring an external magnetic field. Our results establish quantum emitters in hBN as a robust platform for multifunctional quantum sensing under realistic operating conditions.