Abstract Quantum metrology offers significant improvements in several quantum technologies. In this work, we propose a Gaussian quantum metrology protocol assisted by initial position-momentum correlations (PM). We employ a correlated Gaussian wave packet as a probe to examine the dynamics of Quantum Fisher Information (QFI) and purity based on PM correlations to demonstrate how to estimate the PM correlations and, more importantly, to unlock its potential applications such as a resource to enhance quantum thermometry. In the low-temperature regime, we find an improvement in the thermometry of the surrounding environment when the original system exhibits a non-null initial correlation (correlated Gaussian state). In addition, we explore the connection between the loss of purity and the gain in QFI during the process of estimating the effective environment coupling and its effective temperature.
Abstract Quantum metrology offers significant improvements in several quantum technologies. In this work, we propose a Gaussian quantum metrology protocol assisted by initial position-momentum correlations (PM). We employ a correlated Gaussian wave packet as a probe to examine the dynamics of Quantum Fisher Information (QFI) and purity based on PM correlations to demonstrate how to estimate the PM correlations and, more importantly, to unlock its potential applications such as a resource to enhance quantum thermometry. In the low-temperature regime, we find an improvement in the thermometry of the surrounding environment when the original system exhibits a non-null initial correlation (correlated Gaussian state). In addition, we explore the connection between the loss of purity and the gain in QFI during the process of estimating the effective environment coupling and its effective temperature.
Abstract Gaussian quantum probes have been widely used in quantum metrology and thermometry, where the goal is to estimate the temperature of an environment with which the probe interacts. It was recently shown that introducing initial position–momentum (PM) correlations in such probes can enhance the estimation precision compared to standard, uncorrelated Gaussian states. Motivated by these findings, we investigate whether PM correlations can also be advantageous in a simultaneous estimation setting, specifically, when estimating both the PM correlations themselves and the effective environment temperature that interacts with the probe. Using the quantum Fisher information matrix, we derive new precision bounds for this joint estimation task. Additionally, we demonstrate that such correlations can serve as a resource to improve temperature estimation within this multiparameter context. Finally, we analyze the compatibility between the two parameters, establishing conditions under which the derived bounds can be saturated. Graphical abstract
Gaussian quantum states and channels are pivotal across many branches of quantum science and their applications, including the processing and storage of quantum information, the investigation of thermodynamics in the quantum regime, and quantum computation. The great advantage is that Gaussian states are experimentally accessible via their first and second statistical moments. In this work, we investigate parameter estimation for Gaussian states, in which the probe-state preparation stage involves two noncommutative Gaussian measurements on the position and momentum observables, introducing tunable parameters. The influence of these noncommutative Gaussian measurements is investigated through the quantum Fisher information (QFI). We showed that the QFI for characterizing Gaussian channels can be increased by adjusting the uncertainty parameters in the preparation of the probe state. Furthermore, if the probe is initially in a thermal state, probe-state preparation may generate quantum coherence in its energy basis. We showed that not only does the amount of coherence affect the improvement of the QFI, but also the rate of change of the coherence with respect to the parameter to be estimated. The proposed probe-state protocol is applied to two paradigmatic single-mode Gaussian channels, the attenuator and amplification channels, which are building blocks of Gaussian quantum information. Our results contribute to the use of coherence in quantum metrology and are experimentally feasible in quantum-optical devices.
We investigate a quantum metrological protocol operating in a non-Markovian environment by employing the quantum Brownian motion (QBM) model, in which the system is linearly coupled to a reservoir of harmonic oscillators. Specifically, we use a position-momentum (PM) correlated Gaussian state as a probe to examine how memory effects influence the evolution of the system's covariance matrix in the weak coupling regime under both high- and low-temperature conditions. To confirm the presence of non-Markovian behavior, we apply two well-established non-Markovianity quantifiers. Furthermore, we estimate both the channel's sample temperature and its non-Markovianity witness parameter. Our results demonstrate that non-Markovianity and PM correlations can jointly be valuable resources to enhance metrological performance.
We investigate a nonequilibrium quantum thermometry protocol in which an ensemble of qubits, acting as temperature probes, is weakly coupled to a macroscopic thermal bath. The temperature of the bath, the parameter of interest, is encoded in the dissipator of a Markovian thermalization process. For some relevant initial states, we observe a peak in the Quantum Fisher Information (QFI) during the transient of the thermalization, indicating enhanced sensitivity in early-time dynamics. This effect becomes more pronounced at higher bath temperatures and is further enhanced when the initial reduced state of the qubits has a large ground-state population and/or it is highly coherent. We also focus on the role of initial quantum correlations in the thermometric performance, which emerge as a central feature of this work. We find strong numerical evidence that, given same single-qubit reduced states, the inclusion of quantum correlations among the qubits of the ensemble always yields an enhanced QFI. Moreover, even if none of the considered states outperform the (pure, separable) ground state, maximally entangled states display QFIs values remarkably close to the standard quantum limit when probing extremely hot thermal baths. Finally, although the Markovian dynamics does not permit superlinear scaling of the QFI with the number of probes, we identify the most effective initial states for designing high-precision quantum thermometers within this setting. We also provide concrete guidelines for experimental implementations.
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.
Quantum metrology exploits quantum correlations to make precise measurements with limited particle numbers. By utilizing inter- and intramode correlations in an optical interferometer, we find a state that combines entanglement and squeezing to give a sevenfold enhancement in the quantum Fisher information (QFI)---a metric related to the precision---over the shot-noise limit, for low photon numbers. Motivated by practicality we then look at the squeezed cat state, which has recently been made experimentally, and shows further precision gains over the shot-noise limit and a threefold improvement in the QFI over the optimal Gaussian state. We present a conceptually simple measurement scheme that saturates the QFI, and we demonstrate a robustness to loss for small photon numbers. The squeezed cat state can therefore give a significant precision enhancement in optical quantum metrology in practical and realistic conditions.