Operational quantum physics

Lecture Notes in Physics: Monographs 31 ......Page 1
Operational Quantum Physics ......Page 3
Preface ......Page 7
Contents ......Page 9
Prologue ......Page 13
1.1. Statistical Analysis of an Experiment ......Page 17
1.2. pov Measures Arising from Actual Measurements ......Page 19
1.3. Conceptual Problems Requiring pov Measures ......Page 24
1.4. New Possibilities Envisaged with pov Measures ......Page 28
2. Historical Survey ......Page 29
1.1. Preliminaries ......Page 31
1.2. States and Observables ......Page 35
2.1. Unsharp Properties ......Page 37
2.2. Coexistence ......Page 38
2.3. Constructing pov Measures from pv Measures ......Page 41
2.4. Neumark's Theorem ......Page 43
2.5. Symmetric Operators and Contractions ......Page 44
3. Quantum Measurement Theory ......Page 46
3.1. Operations ......Page 47
3.2. State Transformers ......Page 49
3.3. Measurements ......Page 51
3.4. The Standard Model ......Page 54
3.5. Repeatable Measurements ......Page 56
4. Individual Interpretation of Quantum Mechanics ......Page 58
III. Observables ......Page 61
1. Observables as Covariant Objects ......Page 62
2.1. Covariance Properties ......Page 65
2.2. Sharp Position and Momentum ......Page 67
2.3. Unsharp Position and Momentum ......Page 71
2.4. Phase Space Observables ......Page 72
3.1. Covariance Properties ......Page 77
3.2. Orbital Angular Momentum ......Page 79
3.3. Spin ......Page 82
3.4. Angle Observables ......Page 85
4. Energy and Time ......Page 89
4.1. Energy ......Page 90
4.2. Time ......Page 91
5.1. Photon Number and Phase ......Page 94
5.2. Joint Observables for the Quadrature Components ......Page 100
5.3. Photon Localisation ......Page 104
1. Continuous Observables ......Page 107
2.1. Coexistent Observables ......Page 113
2.2. Examples ......Page 114
2.3. Complementary Observables ......Page 116
2.4. Coupling Properties of Position and Momentum ......Page 119
2.5. The Heisenberg Interpretation of the Uncertainty Relations ......Page 120
2.6. Coexistence of Complementary Spin Observables ......Page 121
3. Measurements and Conservation Laws ......Page 122
3.1. Repeatable Measurements and Conservation Laws ......Page 123
3.2. Spin Measurements and Rotation Invariance ......Page 124
3.3. Position Measurements and Momentum Conservation ......Page 126
V. Uncertainty ......Page 129
1. Coarse-Graining ......Page 130
2. Informational Completeness ......Page 132
3.1. Quantum Indeterminism and Classicality Conditions ......Page 136
3.2. Measurement: Disturbance Versus Information Gain ......Page 139
3.3. Unsharpness in Phase Space Inference ......Page 140
3.4. Impossibility of Individual State Determination ......Page 143
4.1. Variance ......Page 146
4.2. Alternative Measures of Uncertainty ......Page 149
4.3. Entropy ......Page 151
1. Representations of States as Phase Space Functions ......Page 157
2. Joint Position-Momentum Measurement ......Page 162
2.1. The Model ......Page 163
2.2. Indeterminacy Relations ......Page 164
2.3. Mutual Disturbance ......Page 166
2.4. Repeatability Features ......Page 167
3.1. Classical Measurement Situation ......Page 168
3.2. Approximately Ideal Measurements ......Page 171
1. Stern-Gerlach Experiment ......Page 177
1.1. Ideal Field ......Page 179
1.2. Realistic Magnetic Field ......Page 183
1.3. Proper Screen Observables ......Page 185
2. Informationally Complete Polarisation Measurement ......Page 186
3.1. Photon Counting and a Lossless Beam Splitter ......Page 189
3.2. First Kind Measurements of the Photon Number ......Page 192
3.3. Measurement of the Photon Number in a Microwave Cavity ......Page 198
3.4. Phase Distributions from Number Statistics ......Page 201
3.5. Nondegenerate Amplification and Two-Mode Squeezing ......Page 203
3.6. Homodyne Detection ......Page 204
3.7. Joint Measurement of the Quadrature Components ......Page 207
3.8. Atomic Position Measurement ......Page 209
4. Wave-Particle Duality of Photons ......Page 211
4.1. Photon Split-Beam Experiments ......Page 212
4.2. Joint Path-Interference Measurements for Single Photons ......Page 218
Epilogue ......Page 225
References ......Page 227
Notations ......Page 237
Subject Index ......Page 239