经典与量子信息论 英文版PDF电子书下载

1 Probability basics 1

1.1 Events,event space,and probabilities 1

1.2 Combinatorics 8

1.3 Combined,joint,and conditional probabilities 11

1.4 Exercises 18

2 Probability distributions 20

2.1 Mean and variance 20

2.2 Exponential,Poisson,and binomial distributions 22

2.3 Continuous distributions 26

2.4 Uniform,exponential,and Gaussian(normal)distributions 26

2.5 Central-limit theorem 33

2.6 Exercises 35

3 Measuring information 37

3.1 Making sense of information 38

3.2 Measuring information 40

3.3 Information bits 43

3.4 Rényi'sfake coin 45

3.5 Exercises 49

4 Entropy 50

4.1 From Boltzmann to Shannon 50

4.2 Entropyindice 53

4.3 Language entropy 57

4.4 Maximum entropy(discrete source) 63

4.5 Exercises 67

5 Mutual information and more entropies 69

5.1 Joint and conditional entropies 69

5.2 Mutual information 75

5.3 Relative entropy 79

5.4 Exercises 82

6 Differential entropy 84

6.1 Entropy of continuous sources 84

6.2 Maximum entropy(continuous source) 90

6.3 Exercises 94

7 Algorithmic entropy and Kolmogorov complexity 96

7.1 Defining algorithmic entropy 96

7.2 The Turingmachine 97

7.3 Universal Turing machine 107

7.4 Kolmogorov complexity 111

7.5 Kolmogorov complexity vs.Shannon's entropy 123

7.6 Exercises 125

8 Information coding 127

8.1 Coding numbers 127

8.2 Coding language 129

8.3 The Morse code 132

8.4 Mean code length and coding efficiency 136

8.5 Optimizing coding efficiency 138

8.6 Shannon's source-coding theorem 142

8.7 Exercises 149

9 Optimal coding and compression 151

9.1 Huffman codes 151

9.2 Data compression 156

9.3 Block codes 162

9.4 Exercises 177

10 Integer,arithmetic,and adaptive coding 179

10.1 Integer coding 179

10.2 Arithmetic coding 185

10.3 Adaptive Huffman coding 192

10.4 Lempel-Ziv coding 200

10.5 Exercises 207

11 Error correction 208

11.1 Communication channel 208

11.2 Linear block codes 210

11.3 Cyclic codes 217

11.4 Error-correction code types 219

11.5 Corrected bit-error-rate 226

11.6 Exercises 230

12 Channel entropy 232

12.1 Binary symmetric channel 232

12.2 Nonbinary and asymmetric discrete channels 234

12.3 Channel entropy and mutual information 238

12.4 Symbol error rate 242

12.5 Exercises 244

13 Channel capacity and coding theorem 245

13.1 Channel capacity 245

13.2 Typical sequences and the typical set 252

13.3 Shannon's channel coding theorem 255

13.4 Exercises 263

14 Gaussian channel and Shannon-Hartley theorem 264

14.1 Gaussian channel 264

14.2 Nonlinear channel 277

14.3 Exercises 282

15 Reversible computation 283

15.1 Maxwell's demon and Landauer's principle 283

15.2 From computer architecture to logic gates 288

15.3 Reversible logic gates and computation 297

15.4 Exercises 302

16 Quantum bits and quantum gates 304

16.1 Quantum bits 304

16.2 Basic computations with 1-qubit quantum gates 310

16.3 Quantum gates with multiple qubit inputs and outputs 315

16.4 Quantum circuits 322

16.5 Tensor products 327

16.6 Noncloning theorem 330

16.7 Exercises 331

17 Quantum measurements 333

17.1 Dirac notation 333

17.2 Quantum measurements and types 343

17.3 Quantum measurements on joint states 351

17.4 Exercises 355

18 Qubit measurements,superdense coding,and quantum teleportation 356

18.1 Measuring single qubits 356

18.2 Measuring n-qubits 361

18.3 Bell state measurement 365

18.4 Superdense coding 366

18.5 Quantum teleportation 367

18.6 Distributed quantum computing 374

18.7 Exercises 376

19 Deutsch-Jozsa,quantum Fourier transform,and Grover quantum database search algorithms 378

19.1 Deutsch algorithm 378

19.2 Deutsch-Jozsa algorithm 381

19.3 Quantum Fourier transform algorithm 383

19.4 Grover quantum database search algorithm 389

19.5 Exercises 398

20 Shor's factorization algorithm 399

20.1 Phase estimation 400

20.2 Order finding 405

20.3 Continued fraction expansion 408

20.4 From order finding to factorization 410

20.5 Shor's factorization algorithm 415

20.6 Factorizing N=15 and other nontrivial composites 417

20.7 Public-key cryptography 424

20.8 Exercises 429

21 Quantum information theory 431

21.1 Von Neumann entropy 431

21.2 Relative,joint,and conditional entropy,and mutual information 437

21.3 Quantum communication channel and Holevo bound 450

21.4 Exercises 454

22 Quantum data compression 457

22.1 Quantum data compression and fidelity 457

22.2 Schumacher's quantum coding theorem 464

22.3 A graphical and numerical illustration of Schumacher's quantum coding theorem 469

22.4 Exercises 474

23 Quantum channel noise and channel capacity 475

23.1 Noisy quantum channels 475

23.2 The Holevo-Schumacher-Westmoreland capacity theorem 481

23.3 Capacity of some quantum channels 487

23.4 Exercises 493

24 Quantum error correction 496

24.1 Quantum repetition code 496

24.2 Shor code 503

24.3 Calderbank-Shor-Steine(CSS)codes 509

24.4 Hadamard-Steane code 514

24.5 Exercises 521

25 Classical and quantum cryptography 523

25.1 Message encryption,decryption,and code breaking 524

25.2 Encryption and decryption with binary numbers 527

25.3 Double-key encryption 532

25.4 Cryptography without key exchange 534

25.5 Public-key cryptography and RSA 536

25.6 Data encryption standard(DES)and advanced encryption standard(AES) 541

25.7 Quantum cryptography 543

25.8 Electromagnetic waves,polarization states,photons,and quantum measurements 544

25.9 A secure photon communication channel 554

25.10 The BB84 protocol for QKD 556

25.11 The B92 protocol 558

25.12 The EPR protocol 559

25.13 Is quantum cryptography"invulnerable?" 562

Appendix A(Chapter 4)Boltzmann's entropy 565

Appendix B(Chapter 4)Shannon's entropy 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)Kraft-McMillan inequality 589

Appendix G(Chapter 9)Overview of data compression standards 591

Appendix H(Chapter 10)Arithmetic coding algorithm 605

Appendix I(Chapter 10)Lempel-Ziv distinctparsing 610

Appendix J(Chapter 11)Error-correction 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 codingtheorem 62lAppendix 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)Two-qubit 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 N=21 through Shor's algorithm 653

Appendix T(Chapter 20)Modular arithmetic and Euler's theorem 656

Appendix U(Chapter 21)Klein's inequality 660

Appendix V(Chapter 21)Schmidt decomposition of joint pure states 662

Appendix W(Chapter 21)Statepurification 664

Appendix X(Chapter 21)Holevo bound 666

Appendix Y(Chapter 25)Polynomial byte representation and modular multiplication 672

Index 676