Book contents
- Frontmatter
- Contents
- Foreword
- Introduction
- Acknowledgments
- 1 Probability basics
- 2 Probability distributions
- 3 Measuring information
- 4 Entropy
- 5 Mutual information and more entropies
- 6 Differential entropy
- 7 Algorithmic entropy and Kolmogorov complexity
- 8 Information coding
- 9 Optimal coding and compression
- 10 Integer, arithmetic, and adaptive coding
- 11 Error correction
- 12 Channel entropy
- 13 Channel capacity and coding theorem
- 14 Gaussian channel and Shannon–Hartley theorem
- 15 Reversible computation
- 16 Quantum bits and quantum gates
- 17 Quantum measurements
- 18 Qubit measurements, superdense coding, and quantum teleportation
- 19 Deutsch–Jozsa, quantum Fourier transform, and Grover quantum database search algorithms
- 20 Shor's factorization algorithm
- 21 Quantum information theory
- 22 Quantum data compression
- 23 Quantum channel noise and channel capacity
- 24 Quantum error correction
- 25 Classical and quantum cryptography
- Appendix A (Chapter 4) Boltzmann's entropy
- Appendix B (Chapter 4) Shannon's entropy
- Appendix C (Chapter 4) Maximum entropy of discrete sources
- Appendix D (Chapter 5) Markov chains and the second law of thermodynamics
- Appendix E (Chapter 6) From discrete to continuous entropy
- Appendix F (Chapter 8) Kraft–McMillan inequality
- Appendix G (Chapter 9) Overview of data compression standards
- Appendix H (Chapter 10) Arithmetic coding algorithm
- Appendix I (Chapter 10) Lempel–Ziv distinct parsing
- Appendix J (Chapter 11) Error-correction capability of linear block codes
- Appendix K (Chapter 13) Capacity of binary communication channels
- Appendix L (Chapter 13) Converse proof of the channel coding theorem
- Appendix M (Chapter 16) Bloch sphere representation of the qubit
- Appendix N (Chapter 16) Pauli matrices, rotations, and unitary operators
- Appendix O (Chapter 17) Heisenberg uncertainty principle
- Appendix P (Chapter 18) Two-qubit teleportation
- Appendix Q (Chapter 19) Quantum Fourier transform circuit
- Appendix R (Chapter 20) Properties of continued fraction expansion
- Appendix S (Chapter 20) Computation of inverse Fourier transform in the factorization of N = 21 through Shor's algorithm
- Appendix T (Chapter 20) Modular arithmetic and Euler's theorem
- Appendix U (Chapter 21) Klein's inequality
- Appendix V (Chapter 21) Schmidt decomposition of joint pure states
- Appendix W (Chapter 21) State purification
- Appendix X (Chapter 21) Holevo bound
- Appendix Y (Chapter 25) Polynomial byte representation and modular multiplication
- Index
Foreword
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Foreword
- Introduction
- Acknowledgments
- 1 Probability basics
- 2 Probability distributions
- 3 Measuring information
- 4 Entropy
- 5 Mutual information and more entropies
- 6 Differential entropy
- 7 Algorithmic entropy and Kolmogorov complexity
- 8 Information coding
- 9 Optimal coding and compression
- 10 Integer, arithmetic, and adaptive coding
- 11 Error correction
- 12 Channel entropy
- 13 Channel capacity and coding theorem
- 14 Gaussian channel and Shannon–Hartley theorem
- 15 Reversible computation
- 16 Quantum bits and quantum gates
- 17 Quantum measurements
- 18 Qubit measurements, superdense coding, and quantum teleportation
- 19 Deutsch–Jozsa, quantum Fourier transform, and Grover quantum database search algorithms
- 20 Shor's factorization algorithm
- 21 Quantum information theory
- 22 Quantum data compression
- 23 Quantum channel noise and channel capacity
- 24 Quantum error correction
- 25 Classical and quantum cryptography
- Appendix A (Chapter 4) Boltzmann's entropy
- Appendix B (Chapter 4) Shannon's entropy
- Appendix C (Chapter 4) Maximum entropy of discrete sources
- Appendix D (Chapter 5) Markov chains and the second law of thermodynamics
- Appendix E (Chapter 6) From discrete to continuous entropy
- Appendix F (Chapter 8) Kraft–McMillan inequality
- Appendix G (Chapter 9) Overview of data compression standards
- Appendix H (Chapter 10) Arithmetic coding algorithm
- Appendix I (Chapter 10) Lempel–Ziv distinct parsing
- Appendix J (Chapter 11) Error-correction capability of linear block codes
- Appendix K (Chapter 13) Capacity of binary communication channels
- Appendix L (Chapter 13) Converse proof of the channel coding theorem
- Appendix M (Chapter 16) Bloch sphere representation of the qubit
- Appendix N (Chapter 16) Pauli matrices, rotations, and unitary operators
- Appendix O (Chapter 17) Heisenberg uncertainty principle
- Appendix P (Chapter 18) Two-qubit teleportation
- Appendix Q (Chapter 19) Quantum Fourier transform circuit
- Appendix R (Chapter 20) Properties of continued fraction expansion
- Appendix S (Chapter 20) Computation of inverse Fourier transform in the factorization of N = 21 through Shor's algorithm
- Appendix T (Chapter 20) Modular arithmetic and Euler's theorem
- Appendix U (Chapter 21) Klein's inequality
- Appendix V (Chapter 21) Schmidt decomposition of joint pure states
- Appendix W (Chapter 21) State purification
- Appendix X (Chapter 21) Holevo bound
- Appendix Y (Chapter 25) Polynomial byte representation and modular multiplication
- Index
Summary
It is always a great opportunity and pleasure for a professor to introduce a new textbook. This one is especially unusual, in a sense that, first of all, it concerns two fields, namely, classical and quantum information theories, which are rarely taught altogether with the same reach and depth. Second, as its subtitle indicates, this textbook primarily addresses the telecom scientist. Being myself a quantum-mechanics teacher but not being conversant with the current Telecoms paradigm and its community expectations, the task of introducing such a textbook is quite a challenge. Furthermore, both subjects in information theory can be regarded by physicists and engineers from all horizons, including in telecoms, as essentially academic in scope and rather difficult to reconcile in their applications. How then do we proceed from there?
I shall state, firsthand, that there is no need to convince the reader (telecom or physicist or both) about the benefits of Shannon's classical theory. Generally unbeknown to millions of telecom and computer users, Shannon's principles pervade all applications concerning data storage and computer files, digital music and video, wireline and wireless broadband communications altogether. The point here is that classical information theory is not only a must to know from any academic standpoint; it is also a key to understanding the mathematical principles underlying our information society.
Shannon's theory being reputed for its completeness and societal impact, the telecom engineer (and physicist within!) may, therefore, wonder about the benefits of quantum mechanics (QM), when it comes to information.
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- Information
- Classical and Quantum Information TheoryAn Introduction for the Telecom Scientist, pp. xi - xviPublisher: Cambridge University PressPrint publication year: 2009