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Information Geometrical Characterization of Quantum Statistical Models in Quantum Estimation Theory

Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan
Entropy 2019, 21(7), 703; https://doi.org/10.3390/e21070703
Received: 10 June 2019 / Revised: 5 July 2019 / Accepted: 16 July 2019 / Published: 18 July 2019
(This article belongs to the Section Quantum Information)
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Abstract

In this paper, we classify quantum statistical models based on their information geometric properties and the estimation error bound, known as the Holevo bound, into four different classes: classical, quasi-classical, D-invariant, and asymptotically classical models. We then characterize each model by several equivalent conditions and discuss their properties. This result enables us to explore the relationships among these four models as well as reveals the geometrical understanding of quantum statistical models. In particular, we show that each class of model can be identified by comparing quantum Fisher metrics and the properties of the tangent spaces of the quantum statistical model. View Full-Text
Keywords: quantum parameter estimation; quantum Fisher metric; D-invariant model; asymptotically classical model quantum parameter estimation; quantum Fisher metric; D-invariant model; asymptotically classical model
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Suzuki, J. Information Geometrical Characterization of Quantum Statistical Models in Quantum Estimation Theory. Entropy 2019, 21, 703.

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