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Classical and Quantum Information
 
 

Classical and Quantum Information, 1st Edition

 
Classical and Quantum Information, 1st Edition,Dan Marinescu,ISBN9780123838742
 
 
 

  

Academic Press

9780123838742

9780123838759

744

240 X 197

This book covers topics in quantum computing, quantum information theory, and quantum error correction, three important areas of quantum information processing.

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Key Features

Presents recent results in quantum computing, quantum information theory, and quantum error correcting codes.

Covers both classical and quantum information theory and error correcting codes.

The last chapter of the book covers physical implementation of quantum information processing devices.

Covers the mathematical formalism and the concepts in Quantum Mechanics critical for understanding the properties and the transformations of quantum information.

Description

A new discipline, Quantum Information Science, has emerged in the last two decades of the twentieth century at the intersection of Physics, Mathematics, and Computer Science. Quantum Information Processing is an application of Quantum Information Science which covers the transformation, storage, and transmission of quantum information; it represents a revolutionary approach to information processing.

This book covers topics in quantum computing, quantum information theory, and quantum error correction, three important areas of quantum information processing.

Quantum information theory and quantum error correction build on the scope, concepts, methodology, and techniques developed in the context of their close relatives, classical information theory and classical error correcting codes.

Readership

Graduate students, advanced undergraduate students and professionals (postdocs, faculty, industry research staff) in computer science, electrical engineering, physics, applied physics, mathematics, and maybe chemistry.

Dan Marinescu

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.

Affiliations and Expertise

Professor, Computer Science, University of Central Florida

View additional works by Dan C. Marinescu

Classical and Quantum Information, 1st Edition

DEDICATION

PREFACE

CHAPTER 1. Preliminaries

1.1 ELEMENTS OF LINEAR ALGEBRA

1.2 HILBERT SPACES AND DIRAC NOTATIONS

1.3 HERMITIAN AND UNITARY OPERATORS: PROJECTORS

1.4 POSTULATES OF QUANTUM MECHANICS

1.5 QUANTUM STATE POSTULATE

1.6 DYNAMICS POSTULATE

1.7 MEASUREMENT POSTULATE

1.8 LINEAR ALGEBRA AND SYSTEMS DYNAMICS

1.9 SYMMETRY AND DYNAMIC EVOLUTION

1.10 UNCERTAINTY PRINCIPLE AND MINIMUM UNCERTAINTY STATES

1.11 PURE AND MIXED QUANTUM STATES

1.12 ENTANGLEMENT AND BELL STATES

1.13 QUANTUM INFORMATION

1.14 PHYSICAL REALIZATION OF QUANTUM INFORMATION PROCESSING SYSTEMS

1.15 UNIVERSAL COMPUTERS: THE CIRCUIT MODEL OF COMPUTATION

1.16 QUANTUM GATES, CIRCUITS, AND QUANTUM COMPUTERS

1.17 UNIVERSALITY OF QUANTUM GATES: THE SOLOVAY-KITAEV THEOREM

1.18 QUANTUM COMPUTATIONAL MODELS AND QUANTUM ALGORITHMS

1.19 DEUTSCH, DEUTSCH-JOZSA, BERNSTEIN-VAZIRANI, AND SIMON ORACLES

1.20 QUANTUM PHASE ESTIMATION

1.21 WALSH-HADAMARD AND QUANTUM FOURIER TRANSFORMS

1.22 QUANTUM PARALLELISM AND REVERSIBLE COMPUTING

1.23 GROVER SEARCH ALGORITHM

1.24 AMPLITUDE AMPLIFICATION AND FIXED-POINT QUANTUM SEARCH

1.25 ERROR MODELS AND QUANTUM ALGORITHMS

1.26 HISTORY NOTES

1.27 SUMMARY

1.28 EXERCISES AND PROBLEMS

CHAPTER 2. Measurements and Quantum Information

2.1 MEASUREMENTS AND PHYSICAL REALITY

2.2 COPENHAGEN INTERPRETATION OF QUANTUM MECHANICS

2.3 MIXED STATES AND THE DENSITY OPERATOR

2.4 PURIFICATION OF MIXED STATES

2.5 BORN RULE

2.6 MEASUREMENT OPERATORS

2.7 PROJECTIVE MEASUREMENTS

2.8 POSITIVE OPERATOR-VALUED MEASURES (POVMs)

2.9 NEUMARK THEOREM

2.10 GLEASON THEOREM

2.11 MIXED ENSEMBLES AND THEIR TIME EVOLUTION

2.12 BIPARTITE SYSTEMS: SCHMIDT DECOMPOSITION

2.13 MEASUREMENTS OF BIPARTITE SYSTEMS

2.14 OPERATOR-SUM (KRAUS) REPRESENTATION

2.15 ENTANGLEMENT: MONOGAMY OF ENTANGLEMENT

2.16 EINSTEIN-PODOLSKI-ROSEN (EPR) THOUGHT EXPERIMENT

2.17 HIDDEN VARIABLES

2.18 BELL AND CHSH INEQUALITIES

2.19 VIOLATION OF THE BELL INEQUALITY

2.20 ENTANGLEMENT AND HIDDEN VARIABLES

2.21 QUANTUM AND CLASSICAL CORRELATIONS

2.22 MEASUREMENTS AND QUANTUM CIRCUITS

2.23 MEASUREMENTS AND ANCILLA QUBITS

2.24 MEASUREMENTS AND DISTINGUISHABILITY OF QUANTUM STATES

2.25 MEASUREMENTS AND AN AXIOMATIC QUANTUM THEORY

2.26 HISTORY NOTES

2.27 SUMMARY AND FURTHER READINGS

2.28 EXERCISES AND PROBLEMS

CHAPTER 3. Classical and Quantum Information Theory

3.1 THE PHYSICAL SUPPORT OF INFORMATION

3.2 THERMODYNAMIC ENTROPY

3.3 SHANNON ENTROPY

3.4 SHANNON SOURCE CODING

3.5 MUTUAL INFORMATION AND RELATIVE ENTROPY

3.6 FANO’S INEQUALITY AND THE DATA PROCESSING INEQUALITY

3.7 CLASSICAL INFORMATION TRANSMISSION THROUGH DISCRETE CHANNELS

3.8 TRACE DISTANCE AND FIDELITY

3.9 VON NEUMANN ENTROPY

3.10 JOINT, CONDITIONAL, AND RELATIVE VON NEUMANN ENTROPY

3.11 TRACE DISTANCE AND FIDELITY OF MIXED QUANTUM STATES

3.12 ACCESSIBLE INFORMATION IN A QUANTUM MEASUREMENT AND THE HOLEVO BOUND

3.13 NO-BROADCASTING THEOREM FOR GENERAL MIXED STATES

3.14 SCHUMACHER COMPRESSION

3.15 QUANTUM CHANNELS

3.16 QUANTUM ERASURE

3.17 CLASSICAL INFORMATION CAPACITY OF NOISELESS QUANTUM CHANNELS

3.18 ENTROPY EXCHANGE, ENTANGLEMENT FIDELITY, AND COHERENT INFORMATION

3.19 QUANTUM FANO AND DATA PROCESSING INEQUALITIES

3.20 REVERSIBLE EXTRACTION OF CLASSICAL INFORMATION FROM QUANTUM INFORMATION

3.21 NOISY QUANTUM CHANNELS

3.22 HOLEVO-SCHUMACHER-WESTMORELAND NOISY QUANTUM CHANNEL ENCODING THEOREM

3.23 CAPACITY OF NOISY QUANTUM CHANNELS

3.24 ENTANGLEMENT-ASSISTED CAPACITY OF QUANTUM CHANNELS

3.25 ADDITIVITY AND QUANTUM CHANNEL CAPACITY

3.26 APPLICATIONS OF INFORMATION THEORY

3.27 HISTORY NOTES

3.28 SUMMARY AND FURTHER READINGS

3.29 EXERCISES AND PROBLEMS

CHAPTER 4. Classical Error-Correcting Codes

4.1 INFORMAL INTRODUCTION TO ERROR DETECTION AND ERROR CORRECTION

4.2 BLOCK CODES, DECODING POLICIES

4.3 ERROR CORRECTING AND DETECTING CAPABILITIES OF A BLOCK CODE

4.4 ALGEBRAIC STRUCTURES AND CODING THEORY

4.5 LINEAR CODES

4.6 SYNDROME AND STANDARD ARRAY DECODING OF LINEAR CODES

4.7 HAMMING, SINGLETON, GILBERT-VARSHAMOV, AND PLOTKIN BOUNDS

4.8 HAMMING CODES

4.9 PROPER ORDERING AND THE FAST WALSH-HADAMARD TRANSFORM

4.10 REED-MULLER CODES

4.11 CYCLIC CODES

4.12 ENCODING AND DECODING CYCLIC CODES

4.13 THE MINIMUM DISTANCE OF A CYCLIC CODE AND THE BCH BOUND

4.14 BURST ERRORS AND INTERLEAVING

4.15 REED-SOLOMON CODES

4.16 CONVOLUTIONAL CODES

4.17 PRODUCT CODES

4.18 SERIALLY CONCATENATED CODES AND DECODING COMPLEXITY

4.19 PARALLEL CONCATENATED CODES: TURBO CODES

4.20 HISTORY NOTES

4.21 SUMMARY AND FURTHER READINGS

4.22 EXERCISES AND PROBLEMS

CHAPTER 5. Quantum Error-Correcting Codes

5.1 QUANTUM ERROR CORRECTION

5.2 A NECESSARY CONDITION FOR THE EXISTENCE OF A QUANTUM CODE

5.3 QUANTUM HAMMING BOUND

5.4 SCALE-UP AND SLOW-DOWN

5.5 A REPETITIVE QUANTUM CODE FOR A SINGLE BIT-FLIP ERROR

5.6 A REPETITIVE QUANTUM CODE FOR A SINGLE PHASE-FLIP ERROR

5.7 THE NINE-QUBIT ERROR-CORRECTING CODE OF SHOR

5.8 THE SEVEN-QUBIT ERROR-CORRECTING CODE OF STEANE

5.9 AN INEQUALITY FOR REPRESENTATIONS IN DIFFERENT BASES

5.10 CALDERBANK-SHOR-STEANE (CSS) CODES

5.11 THE PAULI GROUP

5.12 STABILIZER CODES

5.13 STABILIZERS FOR PERFECT QUANTUM CODES

5.14 QUANTUM RESTORATION CIRCUITS

5.15 QUANTUM CODES OVER GF(pk)

5.16 QUANTUM REED-SOLOMON CODES

5.17 CONCATENATED QUANTUM CODES

5.18 QUANTUM CONVOLUTIONAL AND QUANTUM TAIL-BITING CODES

5.19 CORRECTION OF TIME-CORRELATED QUANTUM ERRORS

5.20 QUANTUM ERROR-CORRECTING CODES AS SUBSYSTEMS

5.21 BACON-SHOR CODE

5.22 OPERATOR QUANTUM ERROR CORRECTION

5.23 STABILIZERS FOR OPERATOR QUANTUM ERROR CORRECTION

5.24 CORRECTION OF SYSTEMATIC ERRORS BASED ON FIXED-POINT QUANTUM SEARCH

5.25 RELIABLE QUANTUM GATES AND QUANTUM ERROR CORRECTION

5.26 HISTORY NOTES

5.27 SUMMARY AND FURTHER READINGS

5.28 EXERCISES AND PROBLEMS

CHAPTER 6. Physical Realization of Quantum Information Processing Systems

6.1 REQUIREMENTS FOR PHYSICAL IMPLEMENTATIONS OF QUANTUM COMPUTERS

6.2 COLD ION TRAPS

6.3 FIRST EXPERIMENTAL DEMONSTRATION OF A QUANTUM LOGIC GATE

6.4 TRAPPED IONS IN THERMAL MOTION

6.5 ENTANGLEMENT OF QUBITS IN ION TRAPS

6.6 NUCLEAR MAGNETIC RESONANCE: ENSEMBLE QUANTUM COMPUTING

6.7 LIQUID-STATE NMR QUANTUM COMPUTER

6.8 NMR IMPLEMENTATION OF SINGLE-QUBIT GATES

6.9 NMR IMPLEMENTATION OF TWO-QUBIT GATES

6.10 THE FIRST GENERATION NMR COMPUTER

6.11 QUANTUM DOTS

6.12 FABRICATION OF QUANTUM DOTS

6.13 QUANTUM DOT ELECTRON SPINS AND CAVITY QED

6.14 QUANTUM HALL EFFECT

6.15 FRACTIONAL QUANTUM HALL EFFECT

6.17 PHOTONIC QUBITS

6.18 SUMMARY AND FURTHER READINGS

APPENDIX. Observable Algebras and Channels

Glossary

References

Index

Quotes and reviews

"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

 
 
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