Masahito Hayashi Satoshi Ishizaka Akinori Kawachi Gen - Introduction to Quantum Information Science

Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s). This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the centr.;Part I: Hypothesis Testing: Introduction to Part I -- Strong Converse and Steins lemma in quantum hypothesis testing/Tomohiro Ogawa and Hiroshi Nagaoka -- The proper formula for relative entropy and its asymptotics in quantum probability/Fumio Hiai and Dnes Petz -- Strong Converse theorems in Quantum Information Theory/Hiroshi Nagaoka -- Asymptotics of quantum relative entropy from a representation theoretical viewpoint/Masahito Hayashi -- Quantum birthday problems: geometrical aspects of Quantum Random Coding/Akio Fujiwara -- Part II: Quantum Cramr-Rao Bound in Mixed States Model: Introduction to Part II -- A new approach to Cramr-Rao Bounds for quantum state estimation/Hiroshi Nagaoka -- On Fisher information of Quantum Statistical Models/Hiroshi Nagaoka -- On the parameter estimation problem for Quantum Statistical Models/Hiroshi Nagaoka -- A generalization of the simultaneous diagonalization of Hermitian matrices and its relation to Quantum Estimation Theory/Hiroshi Nagaoka -- A linear programming approach to Attainable Cramr-Rao Type Bounds/Masahito Hayashi -- Statistical model with measurement degree of freedom and quantum physics/Masahito Hayashi and Keiji Matsumoto -- Asymptotic Quantum Theory for the Thermal States Family/Masahito Hayashi -- State estimation for large ensembles/Richard D. Gill and Serge Massar -- Part III: Quantum Cramr-Rao Bound in Pure States Model: Introduction to Part III -- Quantum Fisher Metric and estimation for Pure State Models/Akio Fujiwara and Hiroshi Nagaoka -- Geometry of Quantum Estimation Theory/Akio Fujiwara -- An estimation theoretical characterization of coherent states/Akio Fujiwara and Hiroshi Nagaoka -- A geometrical approach to Quantum Estimation Theory/Keiji Matsumoto -- Part IV: Group symmetric approach to Pure States Model: Introduction to Part IV -- Optimal extraction of information from finite quantum ensembles/Serge Massar and Sandu Popescu -- Asymptotic Estimation Theory for a Finite-Dimensional Pure State Model/Masahito Hayashi -- Optimal universal quantum cloning and state estimation/Dagmar Bruss, Artur Ekert, and Chiara Macchiavello -- Bounds for generalized uncertainty of shift parameter/Alexander S. Holevo -- V: Large Deviation Theory in quantum estimation: Introduction to Part V -- On the relation between Kullback divergence and Fisher information: from classical systems to quantum systems/Hiroshi Nagaoka -- Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation/Masahito Hayashi -- Estimating the spectrum of a density operator/Michael Keyl and Reinhard F. Werner -- Part VI: Further topics on quantum statistical inference: Introduction to Part VI -- Optimal quantum clocks/Vladim Buek, R. Derka, and Serge Massar -- Quantum channel identification problem/Akio Fujiwara -- Homodyning as universal detection/Giacomo Mauro DAriano -- On the measurement of qubits/Daniel F.V. James, Paul G. Kwiat, William J. Munro and Andrew G. White.