The likelihood operator and Fisher information in quantum probability

• URL: http://arxiv.org/abs/2502.20055v1
• Date: Thu, 27 Feb 2025 12:54:47 GMT
• Title: The likelihood operator and Fisher information in quantum probability
• Authors: Kalyan B. Sinha, Ritabrata Sengupta,
• Abstract summary: We study the problem of Quantum Likelihood Operators (LO) and their connection with quantum Fisher information (QFI)<n>It is observed that the present approaches to this problem tacitly assume commutativity of parametrised density matrix $rho_theta$ and its derivative.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of Quantum Likelihood Operators (LO) and their connection with quantum Fisher information (QFI). It is observed that the present approaches to this problem tacitly assume commutativity of parametrised density matrix $\rho_\theta$ and its derivative, which, in general, need not be true, and this has nontrivial consequences in QFI. As examples, we discuss the parametrised two-level system exhaustively, and, as a further example, the one-mode coherent states of an infinite-dimensional system.

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