https://doi.org/10.1140/epjp/s13360-024-05517-0
Regular Article
Estimating purity and mixing parameter of the initial state for Tavis–Cumming and dephasing models in multiparameter metrological schemes
1
Faculty of Sciences, LPHE-Modeling and Simulation, Mohammed V University in Rabat, Rabat, Morocco
2
Centre of Physics and Mathematics, Faculty of Sciences, CPM, Mohammed V University in Rabat, Rabat, Morocco
Received:
28
April
2024
Accepted:
29
July
2024
Published online:
9
August
2024
Quantum Fisher information matrix (QFIM) serves as a pivotal metric in multiparameter quantum estimation theory, delineating the utmost precision achievable in discerning parameters within a quantum system. In our investigation, we focus on estimating the purity and mixing parameter of the initial state in Tavis–Cumming and dephasing models within this multiparameter framework. The challenge in deriving analytical expressions for QFIM stems from the predominant reliance on density matrix diagonalization methods in most calculation approaches. To surmount these limitations, we use the Hilbert–Schmidt speed as a potent merit factor for parameter estimation. Through comparative analysis, we evaluate the efficacy of individual versus simultaneous estimation strategies in multiparameter scenarios and illustrate the indispensable role of quantum resources such as entanglement, discord, and coherence in optimizing multiparameter estimation. Our findings underscore the capability of HSS to detect the lower bounds on statistical estimation errors and delineate optimal estimation regions, with highest HSS corresponding to the greatest amount of quantum Fisher information. Furthermore, simultaneous multiparameter estimation exhibits superior performance compared to individual estimation strategies across both systems. Ultimately, the integration of quantum entanglement, quantum discord, and quantum coherence markedly enhances the precision of metrological protocols.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
