Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2507.16742 · The European Physical Journal Plus

Multiparameter estimation with position-momentum correlated Gaussian probes

João C. P. Porto, Carlos H. S. Vieira, Pedro R. Dieguez, I. G. da Paz, Lucas S. Marinho

Published Feb 23, 2026• 0 citations
arXivHTMLPDF

Abstract

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

DOI
10.1140/epjp/s13360-026-07389-y

Related papers

Enhancing Gaussian quantum metrology with position-momentum correlations

João C. P. Porto, Lucas S. Marinho, Pedro R. Dieguez +2 more

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.

arXiv:2408.13060•Physica Scripta•Dec 3, 2024•10 citations

Multiparameter Gaussian quantum metrology

Rosanna Nichols, Pietro Liuzzo-Scorpo, Paul A. Knott +1 more

We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cram\'er-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfill the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.

arXiv:1711.09132•Physical Review A•Jul 11, 2018•130 citations

Temperature and non-Markovian parameter estimation in quantum Brownian motion

João C. P. Porto, Carlos H. S. Vieira, I. G. da Paz +2 more

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.

arXiv:2504.08529•Physical Review A•Sep 19, 2025•0 citations

Multiparameter Quantum Metrology in Molecular Dimers

Omar Bachain, Mohamed Amazioug, Rachid Ahl Laamara

We investigate multiparameter quantum estimation in a molecular dimer composed of two dipole--dipole interacting two-level systems, focusing on the simultaneous estimation of temperature $T$ and detuning $Λ$. By employing a vectorization approach to derive the quantum Fisher information matrix, we analyze the precision limits of both simultaneous and individual estimation strategies. We show that simultaneous estimation outperforms the individual one in the near-resonant and low-temperature regime, where quantum coherence is enhanced, while its advantage is progressively reduced under detuned conditions and increasing temperature. Our results demonstrate that temperature acts as a key control parameter governing both estimation precision providing a unified perspective on quantum metrology. These findings highlight the potential of molecular quantum systems as realistic platforms for multiparameter quantum sensing.

quant-pharXiv:2607.11831•Jul 14, 2026•0 citations

Ultimate precision of joint parameter estimation under noisy Gaussian environment

Bakmou Lahcen, Mohammed Daoud A

The major problem of multiparameter quantum estimation theory is to find an ultimate measurement scheme to go beyond the standard quantum limits that each quasi-classical estimation measurement is limited by. Although, in some specifics quantum protocols without environmental noise, the ultimate sensitivity of a multiparameter quantum estimation can beat the standard quantum limit. However, the presence of noise imposes limitations on the enhancement of precision due to the inevitable existence of environmental fluctuations. Here, we address the motivation behind the usage of Gaussian quantum resources and their advantages in reaching the standard quantum limits under realistic noise. In this context, our work aims to explore the ultimate limits of precision for the simultaneous estimation of a pair of parameters that characterize the displacement channel acting on Gaussian probes and subjected to open dynamics. More precisely, we focus on a general two-mode mixed squeezed displaced thermal state, after reducing it to various Gaussian probes states, like; a two-mode pure squeezed vacuum, two-mode pure displaced vacuum, two-mode mixed displaced thermal, two-mode mixed squeezed thermal. To study the ultimate estimation precision, we evaluate the upper and bottom bound of HCRB in various cases. We find that when the entangled states, two-mode pure squeezed vacuum and two-mode mixed squeezed thermal, are employed as probes states, the upper and bottom bound of HCRB beats the standard quantum limit in the presence of a noisy environment.

arXiv:2203.09847•Mar 18, 2022•0 citations

Multiparameter Quantum Estimation in a Raman-Coupled Two-Qubit System

Omar Bachain, Mohamed Amazioug, Rachid Ahl Laamara

We investigate multiparameter quantum estimation in a Raman-coupled two-qubit system at thermal equilibrium. Analytical expressions for the quantum Fisher information matrix are derived to characterize the simultaneous estimation of the temperature and Raman coupling strength. The corresponding quantum Cramér--Rao bounds are obtained and compared with those of individual estimation strategies. Our results reveal optimal operating regimes determined by the interplay between thermal fluctuations and coherent interactions. In particular, quantum thermometry exhibits a well-defined optimal temperature window, whereas the estimation of the Raman coupling strength is significantly enhanced in the low-temperature and weak-coupling regime. We further show that simultaneous estimation can outperform independent estimation within appropriate parameter regions, highlighting the advantages of multiparameter quantum metrology. These results provide analytical insights into the ultimate precision limits of Raman-coupled two-qubit systems and identify promising operating regimes for quantum sensing and quantum thermometry.

quant-pharXiv:2607.11823•Jul 14, 2026•0 citations
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
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.
We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cram\'er-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfill the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.
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 multiparameter quantum estimation in a molecular dimer composed of two dipole--dipole interacting two-level systems, focusing on the simultaneous estimation of temperature TTT and detuning ΛΛΛ. By employing a vectorization approach to derive the quantum Fisher information matrix, we analyze the precision limits of both simultaneous and individual estimation strategies. We show that simultaneous estimation outperforms the individual one in the near-resonant and low-temperature regime, where quantum coherence is enhanced, while its advantage is progressively reduced under detuned conditions and increasing temperature. Our results demonstrate that temperature acts as a key control parameter governing both estimation precision providing a unified perspective on quantum metrology. These findings highlight the potential of molecular quantum systems as realistic platforms for multiparameter quantum sensing.
The major problem of multiparameter quantum estimation theory is to find an ultimate measurement scheme to go beyond the standard quantum limits that each quasi-classical estimation measurement is limited by. Although, in some specifics quantum protocols without environmental noise, the ultimate sensitivity of a multiparameter quantum estimation can beat the standard quantum limit. However, the presence of noise imposes limitations on the enhancement of precision due to the inevitable existence of environmental fluctuations. Here, we address the motivation behind the usage of Gaussian quantum resources and their advantages in reaching the standard quantum limits under realistic noise. In this context, our work aims to explore the ultimate limits of precision for the simultaneous estimation of a pair of parameters that characterize the displacement channel acting on Gaussian probes and subjected to open dynamics. More precisely, we focus on a general two-mode mixed squeezed displaced thermal state, after reducing it to various Gaussian probes states, like; a two-mode pure squeezed vacuum, two-mode pure displaced vacuum, two-mode mixed displaced thermal, two-mode mixed squeezed thermal. To study the ultimate estimation precision, we evaluate the upper and bottom bound of HCRB in various cases. We find that when the entangled states, two-mode pure squeezed vacuum and two-mode mixed squeezed thermal, are employed as probes states, the upper and bottom bound of HCRB beats the standard quantum limit in the presence of a noisy environment.
We investigate multiparameter quantum estimation in a Raman-coupled two-qubit system at thermal equilibrium. Analytical expressions for the quantum Fisher information matrix are derived to characterize the simultaneous estimation of the temperature and Raman coupling strength. The corresponding quantum Cramér--Rao bounds are obtained and compared with those of individual estimation strategies. Our results reveal optimal operating regimes determined by the interplay between thermal fluctuations and coherent interactions. In particular, quantum thermometry exhibits a well-defined optimal temperature window, whereas the estimation of the Raman coupling strength is significantly enhanced in the low-temperature and weak-coupling regime. We further show that simultaneous estimation can outperform independent estimation within appropriate parameter regions, highlighting the advantages of multiparameter quantum metrology. These results provide analytical insights into the ultimate precision limits of Raman-coupled two-qubit systems and identify promising operating regimes for quantum sensing and quantum thermometry.