Six Quantum Pieces: A First Course in Quantum Physics

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More About This Textbook

Overview

This book is an original first approach to quantum physics, the core of modern physics. It combines the competence of a well-known researcher in quantum information science and the freshness in style of two high school students.

Quantum physics is known to be challenging for two reasons: it describes counter-intuitive phenomena and employs rather advanced mathematics. The description of " traditional" quantum phenomena (the structure of atoms and molecules, the properties of solids, the zoology of sub-atomic particles) does indeed involve the whole formalism. However, some other striking phenomena, somehow the most " typically quantum" ones, can be described using only high school mathematical skills. This approach exploits this fact, thus making it possible for a beginner to tackle mind-boggling experiments like teleportation and the violation of Bell's inequality, and practice notions like superposition, entanglement and decoherence.

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Product Details

  • ISBN-13: 9789814327534
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 9/16/2010
  • Pages: 140
  • Product dimensions: 6.20 (w) x 9.00 (h) x 0.70 (d)

Table of Contents

Foreword xi

Acknowledgments xv

A User's Guide xvii

Notions and Formalism 1

1 Introducing Quantum Physics with Polarization 3

1.1 Polarization of a Light Beam 3

1.1.1 Definition and basic measurement 3

1.1.2 Series of polarizers 4

1.1.3 Polarization in vector notation 6

1.1.4 Polarizing beam-splitters as measurement devices 7

1.2 Polarization of One Photon 9

1.2.1 Describing one photon 9

1.2.2 Computations using Dirac notation 10

1.2.3 The meaning of probabilities 11

1.3 Describing Two Photons 13

1.3.1 Classical composite systems 13

1.3.2 Four states of two photons 13

1.3.3 All the states of two photons 14

1.3.4 The meaning of entanglement 15

1.4 Transformations of States 16

1.5 Summary 17

1.6 The Broader View 18

1.6.1 Vectors 18

1.6.2 Probability 18

1.6.3 Degree of freedom 19

1.7 General References 21

1.8 Solutions to the Exercises 22

Six Pieces 25

2 Quantum Cryptography 27

2.1 One-Time Pad 29

2.2 The Idea of Quantum Key Distribution 30

2.3 The BB84 Protocol 31

2.3.1 The steps of the protocol 31

2.3.2 Statistics from quantum measurements 32

2.3.3 Extracting the secret key 35

2.4 More on Classical Post-Processing 36

2.4.1 Error correction 36

2.4.2 Privacy amplification 37

2.5 Summary 38

2.6 The Broader View 38

2.6.1 The power of Eve and the power of quantum 38

2.6.2 Practical quantum cryptography 39

2.6.3 Information theory 40

2.7 References and Further Reading 40

2.8 Solutions to the Exercises 41

3 Quantum Cloning 47

3.1 The No-Cloning Theorem 47

3.2 Trivial Cloning of Quantum States 48

3.3 Optimal Cloning of Quantum States 49

3.4 Other Quantum Cloning Procedures 50

3.5 Stimulated Emission and Quantum Cloning 51

3.6 Summary 52

3.7 The Broader View 53

3.7.1 Relation with biological cloning 53

3.7.2 Relation with broadcasting in telecommunication 53

3.8 References and Further Reading 54

3.9 Solutions to the Exercises 54

4 Quantum Teleportation 59

4.1 Teleportation Protocol 59

4.2 Study of Information Transfer 62

4.3 Summary 63

4.4 The Broader View 63

4.4.1 Entanglement swapping 63

4.4.2 Physics and science fiction 64

4.5 References and Further Reading 65

4.6 Solutions to the Exercises 66

5 Quantum Correlations and Bell's Inequality 71

5.1 Quantum Description 71

5.1.1 Experimental setup 72

5.1.2 Source of entangled photons 72

5.1.3 Mechanism for correlations" 74

5.2 Attempts at Classical Explanations 74

5.3 Bell's Theorem 75

5.4 Summary 77

5.5 The Broader View 77

5.5.1 The danger of words 77

5.5.2 Incompatible physical quantities 79

5.5.3 True randomness, true secrecy 80

5.5.4 About loopholes 80

5.6 References and Further Reading 82

5.7 Solutions to the Exercises 82

6 The GHZ Argument for Quantum Correlations 87

6.1 Quantum Description 87

6.1.1 The setup 87

6.1.2 Measurement X-X-X 88

6.1.3 Measurement X-Y-Y 90

6.2 Impossibility of Classical Mechanisms for Correlations 91

6.3 Summary 92

6.4 The Broader View 92

6.4.1 Falsification of Leggett's model 92

6.5 References and Further Reading 93

6.6 Solutions to the Exercises 94

7 Measurement and Decoherence 97

7.1 Measurement and Entanglement 97

7.2 Decoherence 99

7.3 Summary 102

7.4 The Broader View 102

7.4.1 The measurement problem 102

7.4.2 Quantum computing 104

7.5 References and Further Reading 106

7.6 Solutions to the Exercises 106

Beyond the Six Pieces 113

8 Other Two-Level Systems 115

8.1 Spin 1/2 115

8.1.1 Spins as intrinsic magnetic moments 115

8.1.2 States of spins 116

8.2 Selected States 118

8.2.1 Two paths: interferometry 119

8.2.2 Two energy levels 122

8.3 Summary 122

8.4 The Broader View 123

8.4.1 Two systems on a single " particle" 123

8.4.2 Ramsey interferometry: pulsed NMR and atomic clocks 123

8.5 References and Further Reading 124

8.6 Solutions to the Exercises 125

9 Link with More Traditional Presentations of Quantum Physics 127

9.1 The Content of Traditional Approaches 127

9.2 Description of Systems with Position and Momentum 128

9.2.1 Position, wave-functions 128

9.2.2 Adding momentum; uncertainty relations 130

9.3 Dynamics of Quantum Systems 130

9.3.1 Schrödinger equation: description 131

9.3.2 Schrödinger equation: solution 132

9.4 Summary 133

9.5 The Broader View 134

9.5.1 The original Einstein - Podolsk - Rosen argument 134

9.6 References and Further Reading 135

Concluding Remarks 137

Index 139

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