Symmetric Logarithmic Derivative Research Articles

Quantum Fisher metric and estimation for pure state models

A statistical parameter estimation theory for quantum pure state models is presented. We first investigate the basic framework of pure state estimation theory and derive quantum counterparts of the Fisher metric. We then formulate a one-parameter estimation theory, based on symmetric logarithmic derivatives, and clarify the differences between pure state models and strictly positive models.

Asymptotically efficient approaches to quantum-mechanical parameter estimation

This paper presents two approaches to quantum-mechanical parameter estimation. For commuting density operators, a maximum-likelihood estimator is described, and its asymptotic properties are discussed, including the asymptotic efficiency. The selection of an observable for noncommuting density operators is considered, and the maximumlikelihood approach is generalized to the case where the symmetric logarithmic derivatives commute. A quantum-mechanical stochastic approximation algorithm is presented, which, under certain conditions, is asymptotically efficient, even if the density operators for different parameter values do not commute. The results are applied to the quantum estimation of unknown frequencies, and the convergence conditions for this problem are discussed.