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International Journal of Theoretical Physics

Quantum Non-Hermitian Sensor for High Metrological Precision Thermometry

Somayyeh Ghorbani, Seyed Mohammad Hosseiny, Milad Norouzi

Published Aug 5, 2026• 0 citations
Publisher
DOI
10.1007/s10773-026-06422-1

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Non-Hermitian systems have been extensively studied in quantum metrology due to their unique properties, such as the skin effects, exceptional points, and the non-reciprocity. It has been demonstrated that although non-Hermitian systems may achieve ultra-high precision of quantum sensing, the measurement precision greatly depends on the position of the coherent drive in the regime of linear response. In this paper, we further investigate how the position of the coherent drive impacts the precision of non-Hermitian sensing in the regime beyond linear response. It is found that in contrast to the linear case, the best possible quantum Fisher information per photon of the sensor does not depend on the position of the coherent drive in the nonlinear perturbation regime.
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.
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.
Non-Hermitian systems have emerged as a powerful paradigm for ultrasensitive sensing, leveraging unique spectral and dynamical properties unmatched in Hermitian physics. While recent theoretical bounds suggest these protocols offer no metrological advantage over Hermitian ones in the ideal shot-noise-limited regime when rigorously accounting for the success probability of non-unitary evolution, their practical utility in realistic experimental conditions has not yet been systematically explored. In this work, we shift the focus toward practical laboratory performance and demonstrate that non-Hermitian sensing protocols can significantly outperform their Hermitian counterparts in the presence of pervasive classical technical noises. This performance gain mainly stems from a strongly enhanced susceptibility that amplifies the signal response, effectively overcoming the precision floor imposed by technical imperfections. By numerically evaluating the Fisher information under technical noise, we further substantiate the regimes where non-Hermitian platforms yield definitive practical gains. Our results reconcile the ongoing debate between fundamental limits and experimental observations, offering a concrete avenue for building high-precision, noise-resilient sensors.