Introduction to quantum information science

• Main Author: Vedral, Vlatko
• Format: eBook Book
• Language: English
• Published: Oxford Oxford University Press 2006; Oxford University Press, Incorporated
• Edition: 1
• Series: Oxford Graduate Texts
• Subjects: Mathematical and Statistical Physics; Quantum communication; Quantum theory; Bekenstein bound; quantum mechanics; Landauer's erasure; quantum entanglement; thermodynamics; Holevo bound; quantum information; quantum communication; quantum algorithms; quantum error correction

In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the s...

Table of Contents:

• 13.3 General conditions -- 13.4 Reliable quantum computation -- 13.5 Quantum error correction considered as a Maxwell's demon -- 13.6 Summary -- 14 Outlook -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W
• 6.5 Relative entropy and thermodynamics -- 6.6 Entropy increase due to erasure -- 6.7 Landauer's erasure and data compression -- 6.8 Summary -- PART II: QUANTUM ENTANGLEMENT -- 7 Quantum entanglement-introduction -- 7.1 The historical background of entanglement -- 7.2 Bell's inequalities -- 7.3 Separable states -- 7.4 Pure states and Bell's inequalities -- 7.5 Mixed states and Bell's inequalities -- 7.6 Entanglement in second quantization -- 7.7 Summary -- 8 Witnessing quantum entanglement -- 8.1 Entanglement witnesses -- 8.2 The Jamiolkowski isomorphism -- 8.3 The Peres-Horodecki criterion -- 8.4 More examples of entanglement witnesses -- 8.5 Summary -- 9 Quantum entanglement in practice -- 9.1 Measurements with a Mach-Zehnder interferometer -- 9.2 Interferometric implementation of Peres-Horodecki criterion -- 9.3 Measuring the .delity between [omitted] and &amp -- #963 -- -- 9.4 Summary -- 10 Measures of entanglement -- 10.1 Distillation of multiple copies of a pure state -- 10.2 Analogy with the Carnot Cycle -- 10.3 Properties of entanglement measures -- 10.4 Entanglement of pure states -- 10.5 Entanglement of mixed states -- 10.6 Measures of entanglement derived from relative entropy -- 10.7 Classical information and entanglement -- 10.8 Entanglement and thermodynamics -- 10.9 Summary -- PART III: QUANTUM COMPUTATION -- 11 Quantum algorithms -- 11.1 Computational complexity -- 11.2 Deutsch's algorithm -- 11.3 Oracles -- 11.4 Grover's search algorithm -- 11.5 Quantum factorization -- 11.6 Summary -- 12 Entanglement, computation and quantum measurements -- 12.1 Optimization of searches using entanglement -- 12.2 Model for quantum measurement -- 12.3 Correlations and quantum measurement -- 12.4 The ultimate limits of computation: the Bekenstein bound -- 12.5 Summary -- 13 Quantum error correction -- 13.1 Introduction -- 13.2 A simple example
• Intro -- Contents -- PART I: CLASSICAL AND QUANTUM INFORMATION -- 1 Classical information -- 1.1 Information and physics -- 1.2 Quantifying information -- 1.3 Data compression -- 1.4 Related measures of information -- 1.5 Capacity of a noisy channel -- 1.6 Summary -- 2 Quantum mechanics -- 2.1 Dirac notation -- 2.2 The qubit, higher dimensions, and the inner product -- 2.3 Hilbert spaces -- 2.4 Projective measurements and operations -- 2.5 Unitary operations -- 2.6 Eigenvectors and eigenvalues -- 2.7 Spectral decomposition -- 2.8 Applications of the spectral theorem -- 2.9 Dirac notation shorthands -- 2.10 The Mach-Zehnder interferometer -- 2.11 The postulates of quantum mechanics -- 2.12 Mixed states -- 2.13 Entanglement -- 2.14 Summary -- 3 Quantum information-the basics -- 3.1 No cloning of quantum bits -- 3.2 Quantum cryptography -- 3.3 The trace and partial-trace operations -- 3.4 Hilbert space extension -- 3.5 The Schmidt decomposition -- 3.6 Generalized measurements -- 3.7 CP-maps and positive operator-valued measurements -- 3.8 The postulates of quantum mechanics revisited -- 3.9 Summary -- 4 Quantum communication with entanglement -- 4.1 Pure state entanglement and Pauli matrices -- 4.2 Dense coding -- 4.3 Teleportation -- 4.4 Entanglement swapping -- 4.5 No instantaneous transfer of information -- 4.6 The extended-Hilbert-space view -- 4.7 Summary -- 5 Quantum information I -- 5.1 Fidelity -- 5.2 Helstrom's discrimination -- 5.3 Quantum data compression -- 5.4 Entropy of observation -- 5.5 Conditional entropy and mutual information -- 5.6 Relative entropy -- 5.7 Statistical interpretation of relative entropy -- 5.8 Summary -- 6 Quantum information II -- 6.1 Equalities and inequalities related to entropy -- 6.2 The Holevo bound -- 6.3 Capacity of a bosonic channel -- 6.4 Information gained through measurements