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
1 - Probability basics
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
Because of the reader's interest in information theory, it is assumed that, to some extent, he or she is relatively familiar with probability theory, its main concepts, theorems, and practical tools. Whether a graduate student or a confirmed professional, it is possible, however, that a good fraction, if not all of this background knowledge has been somewhat forgotten over time, or has become a bit rusty, or even worse, completely obliterated by one's academic or professional specialization!
This is why this book includes a couple of chapters on probability basics. Should such basics be crystal clear in the reader's mind, however, then these two chapters could be skipped at once. They can always be revisited later for backup, should some of the associated concepts and tools present any hurdles in the following chapters. This being stated, some expert readers may yet dare testing their knowledge by considering some of this chapter's (easy) problems, for starters. Finally, any parent or teacher might find the first chapter useful to introduce children and teens to probability.
I have sought to make this review of probabilities basics as simple, informal, and practical as it could be. Just like the rest of this book, it is definitely not intended to be a math course, according to the canonic theorem–proof–lemma–example suite. There exist scores of rigorous books on probability theory at all levels, as well as many Internet sites providing elementary tutorials on the subject.
- Type
- Chapter
- Information
- Classical and Quantum Information TheoryAn Introduction for the Telecom Scientist, pp. 1 - 19Publisher: Cambridge University PressPrint publication year: 2009