Non-Gaussian Dissipative Quantum Thermometry Beyond Gaussian Bounds

TL;DR

This work addresses the fundamental limits of temperature sensing in open quantum systems when using non-Gaussian resources. It develops analytic bounds on the quantum Fisher information in the short-time, dissipative regime for a single-mode bosonic probe initialized in a Fock state and compares it to Gaussian probes under equal energy constraints. The key result is a linear-in-time QFI enhancement for Fock states with a prefactor that scales as $n(n+1)$, while Gaussian probes exhibit quadratic scaling with time, yielding a clear non-Gaussian advantage, especially at low temperatures. The findings are connected to circuit-QED platforms and photon-number-resolving readout, providing a realistic route to implement non-Gaussian quantum thermometry in noisy devices. Overall, the paper bridges theory and experiment by delivering concrete scaling laws, attainable measurement schemes, and guidance for harnessing non-Gaussian resources in practical quantum thermometry.

Abstract

The fundamental metrological limits of temperature sensing in open quantum systems remain largely unresolved, particularly regarding the role of non-Gaussian quantum resources. In this letter, we establish analytic bounds on the quantum Fisher information (QFI) for temperature estimation using non-Gaussian states undergoing dissipative bosonic evolution. By focusing on the short-time regime governed by a time-local master equation, we derive precise scaling laws that elucidate when and how non-Gaussian probes decisively outperform Gaussian states under identical energy constraints. Our analysis uncovers a distinct linear-in-time QFI enhancement unique to Fock states, in contrast to the inherently weaker, quadratic scaling of Gaussian probes. These theoretical insights are substantiated through exact numerical simulations and mapped onto experimentally accessible platforms such as circuit QED. Our results not only clarify the quantum thermometric advantage of non-Gaussianity but also chart a realistic pathway toward harnessing it in noisy quantum technologies.

Figures (5)

• Figure 1: Schematic illustration of quantum thermometry using Gaussian and non-Gaussian probes to estimate the temperature of a bosonic thermal bath.
• Figure 2: QFI for both non-Gaussian (Fock) and Gaussian probe states is plotted as a function of excitation number. The corresponding analytical short-time bounds are also shown for comparison. The mode frequency is set to $\omega = 1.0$. The dissipation rate $\gamma = 0.1$, coupling strength $g=0.05$, and bath temperature $T = 0.5$ (in units of $\omega$) are considered for the analysis.
• Figure 3: Quantum Fisher information (QFI) as a function of bath temperature $T$ for various initial probe states, evaluated at fixed time $t=0.5$, $g=0.05$, $\gamma=0.1$.
• Figure 4: QFI as a function of system–bath coupling strength $g$ for different initial probe states. The evaluation is performed at time $t=0.5$, $T=0.05$, and $\gamma=0.1$.
• Figure 5: QFI as a function of decay rate $\Gamma$ for various initial probe states, computed at time $t=0.5$, $g=0.05$, $T=0.5$.