From spectral structure to sensing limits in quantum thermometry

• URL: http://arxiv.org/abs/2606.25933v1
• Date: Wed, 24 Jun 2026 15:08:11 GMT
• Title: From spectral structure to sensing limits in quantum thermometry
• Abstract summary: We analyze a broad class of quantum systems, ranging from finite spin ensembles and degenerate atoms to confining potentials, quantum walks, and continuous-spectrum universality models.<n>We derive exact scaling laws for the quantum Fisher information, revealing two distinct high-temperature universality classes.<n>We show that sensitivity can be enhanced arbitrarily by engineering degenerate excited states or a quantum walk on a fully connected topology.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The precision of a quantum thermometer is fundamentally constrained by the spectral structure of the probe itself, and a systematic mapping between the configurations of energy levels and thermometric performance provides relevant information to design optimized devices. In this work, we establish such a mapping by analyzing a broad class of quantum systems, ranging from finite spin ensembles and degenerate atoms to confining potentials, quantum walks, and continuous-spectrum models. We derive exact scaling laws for the quantum Fisher information, revealing two distinct high-temperature universality classes: finite-spectrum probes exhibit a $T^{-4}$ decay, while unbounded or continuous spectra yield a slower $T^{-2}$ decay. At low temperatures, we show that sensitivity, though universally exponentially suppressed, can be enhanced arbitrarily by engineering degenerate excited states or a quantum walk on a fully connected topology. By contrast, specific quantum walk topologies provide a distinct enhancement mechanism based on gap engineering, whereby an optimal network size yields an optimized $T^{-2}$ low-temperature scaling. Furthermore, power-law spectra enable tunable scaling of thermometric performance with system size, offering a design principle for optimal probes in specific temperature windows. Our results contribute to transform spectral information into a resource for quantum thermometry, providing both fundamental bounds and practical guidelines to tailored temperature sensing.

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