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Simultaneously achieving Heisenberg- and Landau-limited precision in equilibrium quantum thermometry

Jingyi Fan, Shengshi Pang

Published Oct 23, 2026• 0 citations

Abstract

Equilibrium quantum thermometry seeks to enhance temperature estimation for reservoirs at thermal equilibrium using quantum resources, yet achieving the Heisenberg scaling in a physical protocol remains a significant challenge. Moreover, quantum measurements face an intrinsic limitation arising from an exponential suppression of thermometric sensitivity as the temperature approaches zero. This limitation severely hinders access to high precision in the low-temperature regime. Here, we demonstrate a simple but powerful quantum engineering protocol to overcome these limitations and reach high precision for temperature estimation. By engineering a small subset of central probes and their linear coupling to a larger array of adjacent probes, we show that the composite partition function can be tailored to yield Heisenberg-limited precision for temperature estimation. Critically, we show that this protocol can simultaneously saturate the Landau bound at low temperatures, an inverse quadratic scaling with the temperature, thereby fully exploiting the potential of equilibrium thermometry and circumventing the exponential suppression of thermometric sensitivity in the low-temperature regime. This scheme relies solely on linear interactions, avoiding complicated many-body couplings and ensuring scalability with the number of probes. Moreover, we find that the comparable precision can be achieved using only local measurements on the central probes, substantially reducing the implementation complexity compared to global measurement schemes and offering a promising approach toward high-precision equilibrium thermometry in physical systems.

DOI: 10.1038/s41534-026-01397-7

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Equilibrium quantum thermometry seeks to enhance temperature estimation for reservoirs at thermal equilibrium using quantum resources, yet achieving the Heisenberg scaling in a physical protocol remains a significant challenge. Moreover, quantum measurements face an intrinsic limitation arising from an exponential suppression of thermometric sensitivity as the temperature approaches zero. This limitation severely hinders access to high precision in the low-temperature regime. Here, we demonstrate a simple but powerful quantum engineering protocol to overcome these limitations and reach high precision for temperature estimation. By engineering a small subset of central probes and their linear coupling to a larger array of adjacent probes, we show that the composite partition function can be tailored to yield Heisenberg-limited precision for temperature estimation. Critically, we show that this protocol can simultaneously saturate the Landau bound at low temperatures, an inverse quadratic scaling with the temperature, thereby fully exploiting the potential of equilibrium thermometry and circumventing the exponential suppression of thermometric sensitivity in the low-temperature regime. This scheme relies solely on linear interactions, avoiding complicated many-body couplings and ensuring scalability with the number of probes. Moreover, we find that the comparable precision can be achieved using only local measurements on the central probes, substantially reducing the implementation complexity compared to global measurement schemes and offering a promising approach toward high-precision equilibrium thermometry in physical systems.

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We investigate correlation-enhanced low temperature quantum thermometry. Recent studies have revealed that bath-induced correlations can enhance the low-temperature estimation precision even starting from an uncorrelated state. However, a comprehensive understanding of this enhancement remains elusive. Using the Ramsey interferometry protocol, we illustrate that the estimation precision of

N

thermometers sparsely coupled to a common low-temperature bath can achieve the Heisenberg scaling in the low-temperature regime with only a

π/2

rotation of the measurement axis, in contrast to the standard Ramsey scheme. This result is based on the assumption that interthermometer correlations are induced exclusively by low-frequency noise in the common bath, a condition achievable in practical experimental scenarios. The underlying physical mechanism is clarified, revealing that the Heisenberg scaling arises from the intrinsic nature of the temperature, which is associated solely with the fluctuation of thermal noise. In contrast to the paradigm of independent thermometers, our proposed scheme demonstrates a significant enhancement in precision for low-temperature measurement, making it suitable for precisely measuring the temperature of ultracold systems.

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