Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C∗-Algebras |
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| Authors: | Florio M. Ciaglia,Jü rgen Jost,Lorenz Schwachhö fer |
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| Affiliation: | 1.Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany;2.Faculty of Mathematics, TU Dortmund University, 44221 Dortmund, Germany; |
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| Abstract: | A geometrical formulation of estimation theory for finite-dimensional -algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented. |
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| Keywords: | information geometry, estimation theory, Fisher– Rao metric tensor, Bures– Helstrom metric tensor, Cramer– Rao bound, Helstrom bound, Symmetric Logarithmic Derivative, Differential Geometry of C∗ -algebras |
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