## Classical and Quantum Information Theory: An Introduction for the Telecom ScientistInformation theory lies at the heart of modern technology, underpinning all communications, networking, and data storage systems. This book sets out, for the first time, a complete overview of both classical and quantum information theory. Throughout, the reader is introduced to key results without becoming lost in mathematical details. Opening chapters present the basic concepts and various applications of Shannon's entropy, moving on to the core features of quantum information and quantum computing. Topics such as coding, compression, error-correction, cryptography and channel capacity are covered from classical and quantum viewpoints. Employing an informal yet scientifically accurate approach, Desurvire provides the reader with the knowledge to understand quantum gates and circuits. Highly illustrated, with numerous practical examples and end-of-chapter exercises, this text is ideal for graduate students and researchers in electrical engineering and computer science, and practitioners in the telecommunications industry. Further resources and instructor-only solutions are available at www.cambridge.org/9780521881715. |

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### Contents

1 | |

2 Probability distributions | 20 |

3 Measuring information | 37 |

4 Entropy | 50 |

5 Mutual information and more entropies | 69 |

6 Differential entropy | 84 |

7 Algorithmic entropy and Kolmogorov complexity | 96 |

8 Information coding | 127 |

Appendix B Chapter 4 Shannons entropy1 | 568 |

Appendix C Chapter 4 Maximum entropy of discrete sources | 573 |

Appendix D Chapter 5 Markov chains and the second law of thermodynamics | 581 |

Appendix E Chapter 6 From discrete to continuous entropy | 587 |

Appendix F Chapter 8 KraftMcMillan inequality | 589 |

Appendix G Chapter 9 Overview of data compression standards | 591 |

Appendix H Chapter 10 Arithmetic coding algorithm | 605 |

Appendix I Chapter 10 LempelZiv distinct parsing | 610 |

9 Optimal coding and compression | 151 |

10 Integer arithmetic and adaptive coding | 179 |

11 Error correction | 208 |

12 Channel entropy | 232 |

13 Channel capacity and coding theorem | 245 |

14 Gaussian channel and ShannonHartley theorem | 264 |

15 Reversible computation | 283 |

16 Quantum bits and quantum gates | 304 |

17 Quantum measurements | 333 |

18 Qubit measurements superdense coding and quantum teleportation | 356 |

19 DeutschJozsa quantum Fourier transform and Grover quantum database search algorithms | 378 |

20 Shors factorization algorithm | 399 |

21 Quantum information theory | 431 |

22 Quantum data compression | 457 |

23 Quantum channel noise and channel capacity | 475 |

24 Quantum error correction | 496 |

25 Classical and quantum cryptography | 523 |

Appendix A Chapter 4 Boltzmanns entropy | 565 |

Appendix J Chapter 11 Errorcorrection capability of linear block codes | 614 |

Appendix K Chapter 13 Capacity of binary communication channels | 617 |

Appendix L Chapter 13 Converse proof of the channel coding theorem | 621 |

Appendix M Chapter 16 Bloch sphere representation of the qubit | 625 |

Appendix N Chapter 16 Pauli matrices rotations and unitary operators | 627 |

Appendix O Chapter 17 Heisenberg uncertainty principle | 635 |

Appendix P Chapter 18 Twoqubit teleportation | 637 |

Appendix Q Chapter 19 Quantum Fourier transform circuit | 644 |

Appendix R Chapter 20 Properties of continued fraction expansion | 648 |

Appendix S Chapter 20 Computation of inverse Fourier transform in the factorization of through Shors algorithm | 653 |

Appendix T Chapter 20 Modular arithmetic and Eulers theorem | 656 |

Appendix U Chapter 21 Kleins inequality | 660 |

Appendix V Chapter 21 Schmidt decomposition of joint pure states | 662 |

Appendix W Chapter 21 State purification | 664 |

Appendix X Chapter 21 Holevo bound | 666 |

Appendix Y Chapter 25 Polynomial byte representation and modular multiplication | 672 |

676 | |

### Common terms and phrases

according algorithm Alice and Bob Alice’s Appendix Assume binary bit/symbol block code cbits channel capacity Chapter classical bits codeword coding efﬁciency coding tree coefﬁcients communication channel complex compression conditional entropy consider corresponding cryptography decoding deﬁned deﬁnition deﬁnition in Eq density operator described eigenstates eigenvalues encoding encryption entropy H EPRIBell error correction example factor ﬁdelity ﬁeld ﬁgure ﬁle ﬁmction ﬁnd ﬁnite ﬁrst given Hadamard Huffman coding illustrated inﬁnite information theory input instance integer matrix maximum mean codeword length measurement mutual information observe obtain optimal outcome output parameter Pauli matrices photons polynomial possible POVM preﬁx probability distribution quantum channel quantum circuit quantum computing qubit random referred represents result in Eq satisﬁes sequence Shannon shown in Fig shows source entropy speciﬁc string sufﬁciently symbol Table teleportation tensor theorem transformation unitary vector yields