经典与量子信息论

ForewordIntroduction1 Probability basics1.1 Events,event space,and probabilities1.2 Combinatorics1.3 Combined,joint,and conditional probabilities1.4 Exercises2 Probability distributions2.1 Mean and variance2.2 Exponential,Poisson,and binomial distributions2.3 Continuous distributions2.4 Uniform,exponential,and Gaussian(normal)distributions2.5 Central-limit theorem2.6 Exercises3 Measuring information3.1 Making sense of information3.2 Measuring information3.3 Information bits3.4 Rényi?s fake coin3.5 Exercises4 Entropy4.1 From Boltzmann to Shannon4.2 Entropy in dice4.3 Language entropy4.4 Maximum entropy(discrete source)4.5 Exercises5 Mutual information and more entropies5.1 Joint and conditional entropies5.2 Mutual information5.3 Relative entropy5.4 Exercises6 Differential entropy6.1 Entropy of continuous sources6.2 Maximum entropy(continuous source)6.3 Exercises7 Algorithmic entropy and Kolmogorov complexity7.1 Defining algorithmic entropy7.2 The Turing machine7.3 Universal Turing machine7.4 Kolmogorov complexity7.5 Kolmogorov complexity vs. Shannon?s entropy7.6 Exercises8 Information coding8.1 Coding numbers8.2 Coding language8.3 The Morse code8.4 Mean code length and coding efficiency8.5 Optimizing coding efficiency8.6 Shannon?s source-coding theorem8.7 Exercises9 Optimal coding and compression9.1 Huffman codes9.2 Data compression9.3 Block codes9.4 Exercises10 Integer,arithmetic,and adaptive coding10.1 Integer coding10.2 Arithmetic coding10.3 Adaptive Huffman coding10.4 Lempel-Ziv coding10.5 Exercises11 Error correction11.1 Communication channel11.2 Linear block codes11.3 Cyclic codes11.4 Error-correction code types11.5 Corrected bit-error-rate11.6 Exercises12 Channel entropy12.1 Binary symmetric channel12.2 Nonbinary and asymmetric discrete channels12.3 Channel entropy and mutual information12.4 Symbol error rate12.5 Exercises13 Channel capacity and coding theorem13.1 Channel capacity13.2 Typical sequences and the typical set13.3 Shannon?s channel coding theorem13.4 Exercises14 Gaussian channel and Shannon-Hartley theorem14.1 Gaussian channel14.2 Nonlinear channel14.3 Exercises15 Reversible computation15.1 Maxwell?s demon and Landauer?s principle15.2 From computer architecture to logic gates15.3 Reversible logic gates and computation15.4 Exercises16 Quantum bits and quantum gates16.1 Quantum bits16.2 Basic computations with 1-qubit quantum gates16.3 Quantum gates with multiple qubit inputs and outputs16.4 Quantum circuits16.5 Tensor products16.6 Noncloning theorem16.7 Exercises17 Quantum measurements17.1 Dirac notation17.2 Quantum measurements and types17.3 Quantum measurements on joint states17.4 Exercises18 Qubit measurements,superdense coding,and quantumteleportation18.1 Measuring single qubits18.2 Measuring n-qubits18.3 Bell state measurement18.4 Superdense coding18.5 Quantum teleportation18.6 Distributed quantum computing18.7 Exercises19 Deutsch-Jozsa,quantum Fourier transform,and Grover quantumdatabase search algorithms19.1 Deutsch algorithm19.2 Deutsch-Jozsa algorithm19.3 Quantum Fourier transform algorithm19.4 Grover quantum database search algorithm19.5 Exercises20 Shor?s factorization algorithm20.1 Phase estimation20.2 Order finding20.3 Continued fraction expansion20.4 From order finding to factorization20.5 Shor?s factorization algorithm20.6 Factorizing N=15 and other nontrivial composites20.7 Public-key cryptography20.8 Exercises21 Quantum information theory21.1 Von Neumann entropy21.2 Relative,joint,and conditional entropy,and mutualinformation21.3 Quantum communication channel and Holevo bound21.4 Exercises22 Quantum data compression22.1 Quantum data compression and fidelity22.2 Schumacher?s quantum coding theorem22.3 A graphical and numerical illustration of Schumacher?s quantumcoding theorem22.4 Exercises23 Quantum channel noise and channel capacity23.1 Noisy quantum channels23.2 The Holevo-Schumacher-Westmoreland capacity theorem23.3 Capacity of some quantum channels23.4 Exercises24 Quantum error correction24.1 Quantum repetition code24.2 Shor code24.3 Calderbank-Shor-Steine(CSS)codes24.4 Hadamard-Steane code24.5 Exercises25 Classical and quantum cryptography25.1 Message encryption,decryption,and code breaking25.2 Encryption and decryption with binary numbers25.3 Double-key encryption25.4 Cryptography without key exchange25.5 Public-key cryptography and RSA25.6 Data encryption standard(DES)and advanced encryptionstandard(AES)25.7 Quantum cryptography25.8 Electromagnetic waves,polarization states,photons,and quantummeasurements25.9 A secure photon communication channel25.10 The BB84 protocol for QKD25.11 The B92 protocol25.12 The EPR protocol25.13 Is quantum cryptography?invulnerable??Appendix A(Chapter 4)Boltzmann’s entropyAppendix B(Chapter 4)Shannon’s entropyAppendix C(Chapter 4)Maximum entropy of discrete sourcesAppendix D(Chapter 5)Markov chains and the second law ofthermodynamicsAppendix E(Chapter 6)From discrete to continuous entropyAppendix F(Chapter 8)Kraft-McMillan inequalityAppendix G(Chapter 9)Overview of data compression standardsAppendix H(Chapter 10)Arithmetic coding algorithmAppendix I(Chapter 10)Lempel-Ziv distinct parsingAppendix J(Chapter 11)Error-correction capability of linear blockcodesAppendix K(Chapter 13)Capacity of binary communicationchannelsAppendix L(Chapter 13)Converse proof of the channel codingtheoremAppendix M(Chapter 16)Bloch sphere representation of thequbitAppendix N(Chapter 16)Pauli matrices,rotations,and unitaryoperatorsAppendix O(Chapter 17)Heisenberg uncertainty principleAppendix P(Chapter 18)Two-qubit teleportationAppendix Q(Chapter 19)Quantum Fourier transform circuitAppendix R(Chapter 20)Properties of continued fractionexpansionAppendix S(Chapter 20)Computation of inverse Fourier transform inthe factorization of N=21 through Shor’s algorithmAppendix T(Chapter 20)Modular arithmetic and Euler’s theoremAppendix U(Chapter 21)Klein’s inequalityAppendix V(Chapter 21)Schmidt decomposition of joint purestatesAppendix W(Chapter 21)State purificationAppendix X(Chapter 21)Holevo boundAppendix Y(Chapter 25)Polynomial byte representation and modularmultiplicationIndex

《经典与量子信息论（英文版）》完整地叙述了经典信息论和量子信息论，首先介绍了香农熵的基本概念和各种应用，然后介绍了量子信息和量子计算的核心特点。《经典与量子信息论（英文版）》从经典信息论和量子信息论的角度，介绍了编码、压缩、纠错、加密和信道容量等内容，采用非正式但科学的精确方法，为读者提供了理解量子门和电路的知识。《经典与量子信息论（英文版）》自始至终都在向读者介绍重要的结论，而不是让读者迷失在数学推导的细节中，并且配有大量的实践案例和章后习题，适合电子、通信、计算机等专业的研究生和科研人员学习参考。