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E-grāmata: Classical and Quantum Information

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(Professor, Computer Science, University of Central Florida, USA)
  • Formāts: EPUB+DRM
  • Izdošanas datums: 07-Jan-2011
  • Izdevniecība: Academic Press Inc
  • Valoda: eng
  • ISBN-13: 9780123838759
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Classical and Quantum InformationPalielināt
  • Formāts: EPUB+DRM
  • Izdošanas datums: 07-Jan-2011
  • Izdevniecība: Academic Press Inc
  • Valoda: eng
  • ISBN-13: 9780123838759
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At the intersection of physics, mathematics, and computer science, explain the authors in the preface, the discipline of quantum information science has emerged during the last two decades. The discipline has developed as a response to the limitations and challenges of information processing, which include "[ h]eat dissipation, leakage, and other physical phenomena [ that] limit our ability to build increasingly faster and, implicitly, increasingly smaller solid-state devices...." They continue: "Quantum information is information encoded to some property of quantum particles and obeys the laws of quantum mechanics." With this book, graduate students and researchers are presented with coverage of three areas: quantum computing, quantum information theory, and quantum error correction. Dan C. Marinescu (computer science, U. of Central Florida) and Gabriela M. Marinescu (affiliation not stated) have co-written many books and articles on the subject. Academic Press is an imprint of Elsevier. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)

Recenzijas

"At the intersection of physics, mathematics, and computer science, explain the authors in the preface, the discipline of quantum information science has emerged during the last two decades. The discipline has developed as a response to the limitations and challenges of information processing, which include "[ h]eat dissipation, leakage, and other physical phenomena [ that] limit our ability to build increasingly faster and, implicitly, increasingly smaller solid-state devices...." They continue: "Quantum information is information encoded to some property of quantum particles and obeys the laws of quantum mechanics." With this book, graduate students and researchers are presented with coverage of three areas: quantum computing, quantum information theory, and quantum error correction. Dan C. Marinescu (computer science, U. of Central Florida) and Gabriela M. Marinescu (affiliation not stated) have co-written many books and articles on the subject." --Book News, Reference & Research

Papildus informācija

This book covers topics in quantum computing, quantum information theory, and quantum error correction, three important areas of quantum information processing.
Preface xiii
Chapter 1 Preliminaries
1(132)
1.1 Elements of Linear Algebra
3(7)
1.2 Hilbert Spaces and Dirac Notations
10(5)
1.3 Hermitian and Unitary Operators: Projectors
15(7)
1.4 Postulates of Quantum Mechanics
22(2)
1.5 Quantum State Postulate
24(6)
1.6 Dynamics Postulate
30(5)
1.7 Measurement Postulate
35(3)
1.8 Linear Algebra and Systems Dynamics
38(2)
1.9 Symmetry and Dynamic Evolution
40(2)
1.10 Uncertainty Principle and Minimum Uncertainty States
42(2)
1.11 Pure and Mixed Quantum States
44(2)
1.12 Entanglement and Bell States
46(2)
1.13 Quantum Information
48(6)
1.14 Physical Realization of Quantum Information Processing Systems
54(3)
1.15 Universal Computers: The Circuit Model of Computation
57(5)
1.16 Quantum Gates, Circuits, and Quantum Computers
62(5)
1.17 Universality of Quantum Gates: The Solovay-Kitaev Theorem
67(4)
1.18 Quantum Computational Models and Quantum Algorithms
71(7)
1.19 Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, and Simon Oracles
78(8)
1.20 Quantum Phase Estimation
86(6)
1.21 Walsh-Hadamard and Quantum Fourier Transforms
92(5)
1.22 Quantum Parallelism and Reversible Computing
97(3)
1.23 Grover Search Algorithm
100(13)
1.24 Amplitude Amplification and Fixed-Point Quantum Search
113(8)
1.25 Error Models and Quantum Algorithms
121(1)
1.26 History Notes
122(5)
1.27 Summary
127(1)
1.28 Exercises and Problems
128(5)
Chapter 2 Measurements and Quantum Information
133(88)
2.1 Measurements and Physical Reality
134(4)
2.2 Copenhagen Interpretation of Quantum Mechanics
138(3)
2.3 Mixed States and the Density Operator
141(6)
2.4 Purification of Mixed States
147(2)
2.5 Born Rule
149(2)
2.6 Measurement Operators
151(1)
2.7 Projective Measurements
152(3)
2.8 Positive Operator-Valued Measures (POVMs)
155(3)
2.9 Neumark Theorem
158(2)
2.10 Gleason Theorem
160(3)
2.11 Mixed Ensembles and Their Time Evolution
163(3)
2.12 Bipartite Systems: Schmidt Decomposition
166(2)
2.13 Measurements of Bipartite Systems
168(5)
2.14 Operator-Sum (Kraus) Representation
173(4)
2.15 Entanglement: Monogamy of Entanglement
177(3)
2.16 Einstein-Podolski-Rosen (EPR) Thought Experiment
180(4)
2.17 Hidden Variables
184(6)
2.18 Bell and CHSH Inequalities
190(3)
2.19 Violation of the Bell Inequality
193(4)
2.20 Entanglement and Hidden Variables
197(3)
2.21 Quantum and Classical Correlations
200(1)
2.22 Measurements and Quantum Circuits
201(5)
2.23 Measurements and Ancilla Qubits
206(2)
2.24 Measurements and Distinguishability of Quantum States
208(4)
2.25 Measurements and an Axiomatic Quantum Theory
212(3)
2.26 History Notes
215(1)
2.27 Summary and Further Readings
216(3)
2.28 Exercises and Problems
219(2)
Chapter 3 Classical and Quantum Information Theory
221(124)
3.1 The Physical Support of Information
223(4)
3.2 Thermodynamic Entropy
227(5)
3.3 Shannon Entropy
232(10)
3.4 Shannon Source Coding
242(4)
3.5 Mutual Information and Relative Entropy
246(4)
3.6 Fano's Inequality and the Data Processing Inequality
250(2)
3.7 Classical Information Transmission Through Discrete Channels
252(6)
3.8 Trace Distance and Fidelity
258(1)
3.9 von Neumann Entropy
259(5)
3.10 Joint, Conditional, and Relative von Neumann Entropy
264(2)
3.11 Trace Distance and Fidelity of Mixed Quantum States
266(7)
3.12 Accessible Information in a Quantum Measurement and the Holevo Bound
273(10)
3.13 No-Broadcasting Theorem for General Mixed States
283(4)
3.14 Schumacher Compression
287(1)
3.15 Quantum Channels
288(4)
3.16 Quantum Erasure
292(6)
3.17 Classical Information Capacity of Noiseless Quantum Channels
298(6)
3.18 Entropy Exchange, Entanglement Fidelity, and Coherent Information
304(6)
3.19 Quantum Fano and Data Processing Inequalities
310(4)
3.20 Reversible Extraction of Classical Information from Quantum Information
314(1)
3.21 Noisy Quantum Channels
315(6)
3.22 Holevo-Schumacher-Westmoreland Noisy Quantum Channel Encoding Theorem
321(4)
3.23 Capacity of Noisy Quantum Channels
325(4)
3.24 Entanglement-Assisted Capacity of Quantum Channels
329(4)
3.25 Additivity and Quantum Channel Capacity
333(2)
3.26 Applications of Information Theory
335(2)
3.27 History Notes
337(2)
3.28 Summary and Further Readings
339(3)
3.29 Exercises and Problems
342(3)
Chapter 4 Classical Error-Correcting Codes
345(110)
4.1 Informal Introduction to Error Detection and Error Correction
347(2)
4.2 Block Codes, Decoding Policies
349(4)
4.3 Error Correcting and Detecting Capabilities of a Block Code
353(3)
4.4 Algebraic Structures and Coding Theory
356(9)
4.5 Linear Codes
365(8)
4.6 Syndrome and Standard Array Decoding of Linear Codes
373(4)
4.7 Hamming, Singleton, Gilbert-Varshamov, and Plotkin Bounds
377(6)
4.8 Hamming Codes
383(2)
4.9 Proper Ordering and the Fast Walsh-Hadamard Transform
385(6)
4.10 Reed-Muller Codes
391(5)
4.11 Cyclic Codes
396(5)
4.12 Encoding and Decoding Cyclic Codes
401(13)
4.13 The Minimum Distance of a Cyclic Code and the BCH Bound
414(3)
4.14 Burst Errors and Interleaving
417(3)
4.15 Reed-Solomon Codes
420(12)
4.16 Convolutional Codes
432(5)
4.17 Product Codes
437(3)
4.18 Serially Concatenated Codes and Decoding Complexity
440(2)
4.19 Parallel Concatenated Codes: Turbo Codes
442(5)
4.20 History Notes
447(1)
4.21 Summary and Further Readings
448(3)
4.22 Exercises and Problems
451(4)
Chapter 5 Quantum Error-Correcting Codes
455(108)
5.1 Quantum Error Correction
456(6)
5.2 A Necessary Condition for the Existence of a Quantum Code
462(1)
5.3 Quantum Hamming Bound
463(1)
5.4 Scale-up and Slow-down
464(1)
5.5 A Repetitive Quantum Code for a Single Bit-flip Error
465(7)
5.6 A Repetitive Quantum Code for a Single Phase-flip Error
472(7)
5.7 The Nine-Qubit Error-Correcting Code of Shor
479(2)
5.8 The Seven-Qubit Error-Correcting Code of Steane
481(5)
5.9 An Inequality for Representations in Different Bases
486(5)
5.10 Calderbank-Shor-Steane (CSS) Codes
491(6)
5.11 The Pauli Group
497(3)
5.12 Stabilizer Codes
500(10)
5.13 Stabilizers for Perfect Quantum Codes
510(3)
5.14 Quantum Restoration Circuits
513(2)
5.15 Quantum Codes over GF(pk)
515(4)
5.16 Quantum Reed-Solomon Codes
519(5)
5.17 Concatenated Quantum Codes
524(2)
5.18 Quantum Convolutional and Quantum Tail-Biting Codes
526(10)
5.19 Correction of Time-Correlated Quantum Errors
536(3)
5.20 Quantum Error-Correcting Codes as Subsystems
539(3)
5.21 Bacon-Shor Code
542(5)
5.22 Operator Quantum Error Correction
547(5)
5.23 Stabilizers for Operator Quantum Error Correction
552(2)
5.24 Correction of Systematic Errors Based on Fixed-Point Quantum Search
554(2)
5.25 Reliable Quantum Gates and Quantum Error Correction
556(3)
5.26 History Notes
559(1)
5.27 Summary and Further Readings
559(2)
5.28 Exercises and Problems
561(2)
Chapter 6 Physical Realization of Quantum Information Processing Systems
563(88)
6.1 Requirements for Physical Implementations of Quantum Computers
564(8)
6.2 Cold Ion Traps
572(9)
6.3 First Experimental Demonstration of a Quantum Logic Gate
581(5)
6.4 Trapped Ions in Thermal Motion
586(2)
6.5 Entanglement of Qubits in Ion Traps
588(7)
6.6 Nuclear Magnetic Resonance: Ensemble Quantum Computing
595(2)
6.7 Liquid-State NMR Quantum Computer
597(6)
6.8 NMR Implementation of Single-Qubit Gates
603(2)
6.9 NMR Implementation of Two-Qubit Gates
605(6)
6.10 The First Generation NMR Computer
611(1)
6.11 Quantum Dots
612(7)
6.12 Fabrication of Quantum Dots
619(4)
6.13 Quantum Dot Electron Spins and Cavity QED
623(4)
6.14 Quantum Hall Effect
627(2)
6.15 Fractional Quantum Hall Effect
629(10)
6.16 Alternative Physical Realizations of Topological Quantum Computers
639(2)
6.17 Photonic Qubits
641(6)
6.18 Summary and Further Readings
647(4)
Appendix: Observable Algebras and Channels 651(6)
Glossary 657(32)
References 689(20)
Index 709
Dan C. Marinescu was a Professor of Computer Science at Purdue University in West Lafayette, Indiana from 1984 till 2001 when he joined the Computer Science Department at the University of Central Florida. He has held visiting faculty positions at IBM T. J. Watson Research Center, Yorktown Heights, New York; Institute of Information Sciences, Beijing ; Scalable Systems Division of Intel Corporation; Deutsche Telecom; and INRIA Rocquancourt in France. In 2012 he was a Fulbright Professor at UTFSM (Universidad Tecnica Federico Santa Maria) in Valparaiso, Chile. His research interests cover parallel and distributed systems, cloud computing, scientific computing, and quantum computing and quantum information theory. He has published more than 220 papers in refereed journals and conference proceedings in these areas and authored three books. In 2007 he delivered the Boole Lecture at University College Cork, the school where George Boole taught from 1849 till his death in 1864. Dan Marinescu was the principal investigator of several grants from the National Science Foundation. In 2008 he was awarded a Earnest T.S. Walton fellowship from the Science Foundation of Ireland.
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