Quantum information : an introduction

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Quantum information : an introduction / Masahito Hayashi

資料種別:: 図書
出版情報:: Berlin : Springer, c2006
形態:: xiv, 426 p. ; 24 cm
著者名:: 林, 正人(量子情報理論) <DA18541995>
ISBN:: 9783540302650 [3540302654]
9783642067693 [3642067697] (: pbk)
書誌ID:: BA78147317

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その他の標題:

Introduction to quantum information theory

注記:

"This book is the revised English edition of the Japanese book 'Introduction to Quantum Information Theory', ... originally published by Saiensu-sha, Tokyo, Japan in May 2003"--Pref.
Includes bibliographical references (p. [401]-422) and index

著者名ヨミ:

ハヤシ, マサヒト

主題:

Information theory; Quantum communication; Quantum computers

言語:

英語

目次情報:

Prologue

Mathematical Formulation of Quantum Systems / 1：

Quantum Systems and Linear Algebra / 1.1：

State and Measurement in Quantum Systems / 1.2：

Quantum Two-Level Systems / 1.3：

Composite Systems and Tensor Products / 1.4：

Matrix Inequalities and Matrix Monotone Functions / 1.5：

Information Quantities and Parameter Estimation in Classical Systems / 2：

Information Quantities in Classical Systems / 2.1：

Entropy / 2.1.1：

Relative Entropy / 2.1.2：

Mutual Information / 2.1.3：

The Independent and Identical Condition and Renyi Entropy / 2.1.4：

Extensions to Quantum Systems / 2.2：

Geometry of Probability Distribution Family / 2.3：

Inner Product for Random Variables and Fisher Information / 2.3.1：

Exponential Family and Divergence / 2.3.2：

Estimation in Classical Systems / 2.4：

Type Method and Large Deviation Evaluation / 2.5：

Type Method and Sanov's Theorem / 2.5.1：

Cramer Theorem and Its Application to Estimation / 2.5.2：

Related Books / 2.6：

Quantum Hypothesis Testing and Discrimination of Quantum States / 3：

Two-State Discrimination in Quantum Systems / 3.1：

Discrimination of Plural Quantum States / 3.2：

Asymptotic Analysis of State Discrimination / 3.3：

Hypothesis Testing and Stein's Lemma / 3.4：

Hypothesis Testing by Separable Measurements / 3.5：

Proof of Direct Part of Stein's Lemma / 3.6：

Information Inequalities and Proof of Converse Part of Stein's Lemma / 3.7：

Historical Note / 3.8：

Classical-Quantum Channel Coding (Message Transmission) / 4：

Formulation of the Channel Coding Process in Quantum Systems / 4.1：

Transmission Information in C-Q Channels and Its Properties / 4.1.1：

C-Q Channel Coding Theorem / 4.1.2：

Coding Protocols with Adaptive Decoding and Feedback / 4.2：

Channel Capacities Under Cost Constraint / 4.3：

A Fundamental Lemma / 4.4：

Proof of Direct Part of C-Q Channel Coding Theorem / 4.5：

Proof of Converse Part of C-Q Channel Coding Theorem / 4.6：

Pseudoclassical Channels / 4.7：

State Evolution and Trace-Preserving Completely Positive Maps / 4.8：

Description of State Evolution in Quantum Systems / 5.1：

Examples of Trace-Preserving Completely Positive Maps / 5.2：

State Evolutions in Quantum Two-Level Systems / 5.3：

Information-Processing Inequalities in Quantum Systems / 5.4：

Entropy Inequalities in Quantum Systems / 5.5：

Quantum Information Geometry and Quantum Estimation / 5.6：

Inner Products in Quantum Systems / 6.1：

Metric-Induced Inner Products / 6.2：

Geodesics and Divergences / 6.3：

Quantum State Estimation / 6.4：

Large Deviation Evaluation / 6.5：

Multiparameter Estimation / 6.6：

Quantum Measurements and State Reduction / 6.7：

State Reduction Due to Quantum Measurement / 7.1：

Uncertainty and Measurement / 7.2：

Measurements with Negligible State Demolition / 7.3：

Entanglement and Locality Restrictions / 7.4：

Entanglement and Local Quantum Operations / 8.1：

Fidelity and Entanglement / 8.2：

Entanglement and Information Quantities / 8.3：

Entanglement and Majorization / 8.4：

Distillation of Maximally Entangled States / 8.5：

Dilution of Maximally Entangled States / 8.6：

Unified Approach to Distillation and Dilution / 8.7：

Dilution with Zero-Rate Communication / 8.8：

State Generation from Shared Randomness / 8.9：

Positive Partial Transpose (PPT) Operations / 8.10：

Examples / 8.11：

2 x 2 System / 8.11.1：

Werner State / 8.11.2：

Isotropic State / 8.11.3：

Analysis of Quantum Communication Protocols / 8.12：

Quantum Teleportation / 9.1：

C-Q Channel Coding with Entangled Inputs / 9.2：

C-Q Channel Coding with Shared Entanglement / 9.3：

Quantum Channel Resolvability / 9.4：

Quantum-Channel Communications with an Eavesdropper / 9.5：

C-Q Wiretap Channel / 9.5.1：

Relation to BB84 Protocol / 9.5.2：

Secret Sharing / 9.5.3：

Distillation of Classical Secret Key / 9.5.4：

Proof of Direct Part of C-Q Wiretap Channel Coding Theorem / 9.5.5：

Proof of Converse Part of C-Q Wiretap Channel Coding Theorem / 9.5.6：

Channel Capacity for Quantum-State Transmission / 9.6：

Group Covariance Formulas / 9.7：

d-Dimensional Depolarizing Channel / 9.7.2：

Transpose-Depolarizing Channel / 9.7.3：

Generalized Pauli Channel / 9.7.4：

PNS Channel / 9.7.5：

Erasure Channel / 9.7.6：

Phase-Damping Channel / 9.7.7：

Source Coding in Quantum Systems / 9.8：

Four Kinds of Source Coding Schemes in Quantum Systems / 10.1：

Quantum Fixed-Length Source Coding / 10.2：

Construction of a Quantum Fixed-Length Source Code / 10.3：

Universal Quantum Fixed-Length Source Codes / 10.4：

Universal Quantum Variable-Length Source Codes / 10.5：

Mixed-State Case / 10.6：

Compression by Classical Memory / 10.7：

Compression by Shared Randomness / 10.8：

Relation to Channel Capacities / 10.9：

Limits and Linear Algebra / 10.10：

Limits / A.1：

Singular Value Decomposition and Polar Decomposition / A.2：

Norms of Matrices / A.3：

Convex Functions and Matrix Convex Functions / A.4：

Proof and Construction of Stinespring and Choi-Kraus Representations / A.5：

Proofs of Theorems and Lemmas / B：

Proof of Theorem 3.1 / B.1：

Proof of Theorem 8.2 / B.2：

Proof of Theorem 8.3 / B.3：

Proof of Theorem 8.8 for Mixed States / B.4：

Proof of Theorem 8.9 for Mixed States / B.5：

Proof of Direct Part / B.5.1：

Proof of Converse Part / B.5.2：

Proof of Theorem 9.3 / B.6：

Proof of Lemma 9.4 / B.7：

Proof of Lemma 10.3 / B.8：

Hints and Brief Solutions to Exercises / C：

References

Index

Prologue

Mathematical Formulation of Quantum Systems / 1：

Quantum Systems and Linear Algebra / 1.1：

State and Measurement in Quantum Systems / 1.2：

Quantum Two-Level Systems / 1.3：

Composite Systems and Tensor Products / 1.4：

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