The likelihood operator and Fisher information in quantum probability

2025/02/27 by Kalyan B. Sinha, Sinha, Kalyan B., Ritabrata Sengupta +1
Computer Science · Physics and Astronomy · #81P16 #81P50 #FOS: Mathematics #FOS: Physical sciences #Probability (math.PR) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2502.20055

openalex publication_date 2025/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ρ_θ 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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