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Alexandria Engineering Journal

Simultaneous and individual parameter estimation procedures for a two-twisting axis system

Kareem Alanazi, Nour Zidan, Mona Aldhuwahi, Abeer Alhashash, Salman Saud Alsaeed, H. F. Abdel-Hameed

Published Apr 17, 2025• 1 citation
Publisher

Abstract

We can utilize the Fisher quantum information matrix to evaluate the precision of any multiparametric forecasting methodology, due to the quantum Cramér–Rao bound. Using the density matrix vectorization approach, we examine both simultaneous and individual estimation procedures and the ratios of different estimation strategies. Our investigation takes into account interaction and intrinsic decoherence parameters, along with time, across various parameter combinations in a two-twisting axis model. Our findings suggest that using a simultaneous approach for multiple parameters in multiparameter estimation methods is generally more effective, offering higher precision than strategies that focus on individual parameters.

DOI
10.1016/j.aej.2025.03.127

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We can utilize the Fisher quantum information matrix to evaluate the precision of any multiparametric forecasting methodology, due to the quantum Cramér–Rao bound. Using the density matrix vectorization approach, we examine both simultaneous and individual estimation procedures and the ratios of different estimation strategies. Our investigation takes into account interaction and intrinsic decoherence parameters, along with time, across various parameter combinations in a two-twisting axis model. Our findings suggest that using a simultaneous approach for multiple parameters in multiparameter estimation methods is generally more effective, offering higher precision than strategies that focus on individual parameters.
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In this work, we study the quantum Fisher information on the Heisenberg model in presence of the Dzyaloshinskii–Moriya interaction, basing on the multi-parametric estimation strategy in quantum metrology. First, we employ the density matrix vectorization method with a tool of the quantum Fisher information matrix through quantum Cramer–Rao bound. Second, we show that the multi-parameter quantum Cramer–Rao bound for simultaneous and individual estimation of the temperature and Dzyaloshinskii–Moriya interaction strongly relies on the concepts of the quantum Fisher information matrix. We confirm also the simultaneous strategy that provides a high precision than the individual.
As we enter the era of quantum technologies, quantum estimation theory provides an operationally motivating framework for determining high precision devices in modern technological applications. The aim of any estimation process is to extract information from an unknown parameter embedded in a physical system such as the estimation converges to the true value of the parameter. According to the Cramér-Rao inequality in mathematical statistics, the Fisher information in the case of single-parameter estimation procedures, and the Fisher information matrix in the case of multi-parameter estimation, are the key quantities representing the ultimate precision of the parameters specifying a given statistical model. In quantum estimation strategies, it is usually difficult to derive the analytical expressions of such quantities in a given quantum state. This review provides comprehensive techniques on the analytical calculation of the quantum Fisher information as well as the quantum Fisher information matrix in various scenarios and via several methods. Furthermore, it provides a mathematical transition from classical to quantum estimation theory applied to many freedom quantum systems. To clarify these results, we examine these developments using some examples. Other challenges, including their links to quantum correlations and saturating the quantum Cramér-Rao bound, are also addressed.
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.
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.
Abstract In this article we derive a measure of quantumness in quantum multi-parameter estimation problems. We can show that the ratio between the mean Uhlmann curvature and the Fisher information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cramér–Rao bound. As a testbed for this concept, we consider a quantum many-body system in thermal equilibrium, and explore the quantum compatibility of the model across its phase diagram.