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
Introduction
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
In the world of telecoms, the term information conveys several levels of meaning. It may concern individual bits, bit sequences, blocks, frames, or packets. It may represent a message payload, or its overhead; the necessary extra information for the network nodes to transmit the message payload practically and safely from one end to another. In many successive stages, this information is encapsulated altogether to form larger blocks corresponding to higher-level network protocols, and the reverse all the way down to destination. From any telecom-scientist viewpoint, information represents this uninterrupted flow of bits, with network intelligence to process it. Once converted into characters or pixels, the remaining message bits become meaningful or valuable in terms of acquisition, learning, decision, motion, or entertainment. In such a larger network perspective, where information is well under control and delivered with the quality of service, what could be today's need for any information theory (IT)?
In the telecom research community indeed, there seems to be little interest for information theory, as based on the valid perception that there is nothing new to worry about. While the occasional evocation of Shannon invariably raises passionate group discussions, the professional focus is about the exploitation of bandwidth and network deployment issues.
- Type
- Chapter
- Information
- Classical and Quantum Information TheoryAn Introduction for the Telecom Scientist, pp. xvii - xxPublisher: Cambridge University PressPrint publication year: 2009