Thermal Quantum Sensing: Fisher Information and Work Beyond Gaussian Signals

• URL: http://arxiv.org/abs/2609.09583v1
• Date: Wed, 09 Sep 2026 01:05:53 GMT
• Title: Thermal Quantum Sensing: Fisher Information and Work Beyond Gaussian Signals
• Abstract summary: We establish general relations among the sensitivity of thermal quantum states as quantified by different quantum Fisher information metrics.<n>We show that at high temperature, all monotone QFI metrics coincide to leading order with a universal quantity that can be expressed as the variance of a simple observable.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Understanding how thermal fluctuations modify or suppress quantum-enhanced sensing is a central problem in quantum metrology. Closely related questions arise in quantum thermodynamics, particularly regarding the relation between the work induced by a signal and the information acquired by a sensor. Here, we establish general relations among the sensitivity of thermal quantum states, as quantified by different quantum Fisher information metrics, their temperature dependence, and the work induced by a unitary signal. We further show that, at high temperature, all monotone QFI metrics coincide to leading order with a universal quantity that can be expressed as the variance of a simple observable and itself defines a lesser-known QFI metric. This emergent uniqueness is reminiscent of the uniqueness of classical Fisher information in information geometry. In continuous-variable systems, the infinite-temperature limit is finite and generically non-zero for quadratic Gaussian signals, while it diverges for higher-degree signals. Remarkably, for any purely quadratic signal generator, the infinite-temperature QFI is at least twice the zero-temperature SLD QFI or, equivalently, at least eight times the ground-state variance of the generator. Consequently, the Cramér--Rao lower bound on the estimator variance is reduced by at least a factor of two. We illustrate these results using harmonic chains of bosonic modes relevant to trapped-ion platforms and quantum field-theoretic models.

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