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Quantum query complexity and distributed computing
Röhrig, H.P.
Publication date
2004
Link to publication
Citation for published version (APA):
Röhrig, H. P. (2004). Quantum query complexity and distributed computing. Institute for Logic,
Language and Computation.
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Contents s
Acknowledgmentss xi Publicationss xiii 11 Introduction 1 1.11 Computation is physical 1 1.22 Quantum mechanics 2 1.2.11 States . 2 1.2.22 Evolution 5 1.2.33 Observables 7 1.2.44 Entanglement 12 1.2.55 Perspective 16 1.33 Quantum computation and information 171.3.11 Quantum circuits 17 1.3.22 Quantum black-box algorithms 19
1.3.33 Hallmark results 23
11 Quantum query complexity 25
22 Quantum search 27
2.11 Quantum amplitude amplification 27 2.1.11 Grover's algorithm 27 2.1.22 Amplitude amplification 33
2.22 Convolution products 36 2.33 Search in the density-matrix formalism 41
2.44 Energy levels of a Hamiltonian 48 2.4.11 Sampling from the energy levels 49
2.4.22 Comparing degeneracy degrees 52
2.4.33 Numerical simulations 53
33 Property testing 57
3.11 Introduction 57 3.22 Preliminaries 58 3.33 Separating quantum and classical property testing 59
3.44 An exponential separation 62 3.55 Quantum lower bounds 70 3.66 Further research 73
44 R o b u s t n e s s 75 4.11 Introduction 75 4.22 Robustly recovering all n bits 78
4.33 The multiple-faulty-copies model 83
4.44 Robust polynomials 83 4.55 Discussion and open problems 86
III Distributed quantum computing 87
55 Nonlocality 89
5.11 Introduction 89 5.1.11 Bell inequalities 91
5.1.22 Imperfections . 94
5.22 Definitions 99 5.33 Bounds on multiparty nonlocality 103
5.3.11 Combinatorial bounds 103 5.3.22 Application to the GHZ correlations 105
5.3.33 an addition theorem 108 5.44 Reproducing quantum correlations 110
5.55 Conclusions 115
66 Quantum coin flipping 117
6.11 Introduction 117 6.22 Two-party coin flipping with penalty for cheating 120
6.33 The multiparty model 122 6.3.11 Adversaries 122 6.3.22 The broadcast channel 123
6.44 Multiparty quantum coin-flipping protocols 125
6.55 Lower bound 128 6.5.11 The two-party bound 128
6.5.22 More than two parties 132 6.66 Summary 134 Bibliographyy 135 Indexx 147 Samenvattingg 151 Abstractt 155 be e
