Acknowledgments |
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xi | |
Introduction |
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xiii | |
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1 | (16) |
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6 | (1) |
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Measurements in the Same Direction |
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7 | (1) |
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Measurements in Different Directions |
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7 | (2) |
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9 | (1) |
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10 | (1) |
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11 | (4) |
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15 | (2) |
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17 | (20) |
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Complex Numbers versus Real Numbers |
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17 | (2) |
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19 | (1) |
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19 | (1) |
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20 | (1) |
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21 | (1) |
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21 | (2) |
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23 | (1) |
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Multiplying a Bra by a Ket |
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23 | (1) |
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24 | (1) |
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Bra-Kets and Orthogonality |
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24 | (1) |
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25 | (2) |
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Vectors as Linear Combinations of Basis Vectors |
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27 | (2) |
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29 | (1) |
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30 | (1) |
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30 | (3) |
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33 | (1) |
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Orthogonal and Unitary Matrices |
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34 | (1) |
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35 | (2) |
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37 | (20) |
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37 | (1) |
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Mathematics of Quantum Spin |
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38 | (3) |
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41 | (2) |
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The Basis Associated with a Given Spin Direction |
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43 | (2) |
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Rotating the Apparatus through 60° |
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45 | (1) |
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The Mathematical Model for Photon Polarization |
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46 | (1) |
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The Basis Associated with a Given Polarization Direction |
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47 | (1) |
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The Polarized Filters Experiments |
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47 | (2) |
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49 | (1) |
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50 | (2) |
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Probability Amplitudes and Interference |
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52 | (1) |
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Alice, Bob, Eve, and the BB84 Protocol |
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53 | (4) |
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57 | (14) |
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Alice and Bob's Qubits Are Not Entangled |
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57 | (2) |
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Unentangled Qubits Calculation |
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59 | (2) |
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Entangled Qubits Calculation |
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61 | (1) |
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Superluminal Communication |
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62 | (2) |
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The Standard Basis for Tensor Products |
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64 | (1) |
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How Do You Entangle Qubits? |
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65 | (2) |
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Using the CNOT Gate to Entangle Qubits |
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67 | (1) |
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68 | (3) |
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71 | (18) |
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Entangled Qubits in Different Bases |
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72 | (1) |
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Proof That 1/√[ 1 2]⊗ +1/√2[ 0 1] ⊗ [ 0 1] Equals 1/√2|b0 ⊗ + 1/2√|b1 ⊗ |b1| |
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73 | (2) |
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Einstein and Local Realism |
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75 | (2) |
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Einstein and Hidden Variables |
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77 | (1) |
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A Classical Explanation of Entanglement |
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78 | (1) |
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79 | (1) |
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The Answer of Quantum Mechanics |
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80 | (1) |
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81 | (3) |
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84 | (2) |
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The Ekert Protocol for Quantum Key Distribution |
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86 | (3) |
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6 Classical Logic, Gates, and Circuits |
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89 | (28) |
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90 | (1) |
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91 | (3) |
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94 | (4) |
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98 | (1) |
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99 | (1) |
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100 | (1) |
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101 | (2) |
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103 | (1) |
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103 | (8) |
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111 | (6) |
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7 Quantum Gates and Circuits |
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117 | (24) |
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118 | (1) |
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118 | (2) |
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120 | (1) |
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Quantum Gates Acting on One Qubit |
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121 | (2) |
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Are There Universal Quantum Gates? |
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123 | (1) |
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124 | (2) |
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Quantum Computation versus Classical Computation |
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126 | (1) |
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127 | (2) |
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129 | (3) |
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132 | (3) |
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135 | (6) |
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141 | (30) |
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The Complexity Classes P and NP |
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142 | (2) |
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Are Quantum Algorithms Faster Than Classical Ones? |
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144 | (1) |
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145 | (1) |
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145 | (4) |
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The Kronecker Product of Hadamard Matrices |
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149 | (3) |
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The Deutsch-Jozsa Algorithm |
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152 | (5) |
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157 | (9) |
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166 | (2) |
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168 | (3) |
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9 Impact of Quantum Computing |
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171 | (20) |
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Shor's Algorithm and Cryptanalysis |
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172 | (4) |
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Graver's Algorithm and Searching Data |
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176 | (5) |
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181 | (1) |
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182 | (4) |
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Quantum Supremacy and Parallel Universes |
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186 | (1) |
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187 | (4) |
Index |
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191 | |