## Quantum Information: An OverviewIn one word, this is a responsible book; the rest is commentary. Around 1992 a few of us were led by Charles Bennett into a Garden of Eden of quantum information, communication, and computation. No sooner had we started exploring our surroundings and naming the birds and the beasts, than Peter Shor put an end to that apparent innocence by showing that factoring could be turned—by means of quantum hardware—into a po- nomial task. Fast factoring meant business; everybody seemed to be awfully interested in factoring. Not that anyone had any use for factoring per se, but it seemed that all the world’s secrets were protected by factor-keyed padlocks. Think of all the power and the glory (and something else) that you might get by acting as a consultant to big businesses and government agencies, helping them pick everyone else’s locks and at the same time build unpickable ones (well, nearly unpickable) for themselves. And if one can get an exponential advantage in factoring, wouldn’t an exponential advantage be lying around the corner for practically any other computational task? Quantum infor- tion “and all that” has indeed blossomed in a few years into a wonderful new chapter of physics, comparable in ?avor and scope to thermodynamics. It has alsoturnedintoaveritable“industry”—producingpapers,conferences,exp- iments, e?ects, devices—even proposals for quantum computer architectures. |

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### Contents

IV | 1 |

V | 5 |

VI | 8 |

VII | 11 |

VIII | 14 |

IX | 18 |

X | 23 |

XI | 25 |

LXX | 139 |

LXXI | 140 |

LXXII | 143 |

LXXIII | 144 |

LXXIV | 147 |

LXXV | 148 |

LXXVI | 149 |

LXXVII | 151 |

XII | 29 |

XIII | 32 |

XIV | 34 |

XV | 35 |

XVI | 37 |

XVII | 38 |

XVIII | 39 |

XIX | 41 |

XX | 45 |

XXI | 46 |

XXII | 48 |

XXIII | 49 |

XXIV | 51 |

XXV | 52 |

XXVI | 57 |

XXVII | 61 |

XXVIII | 63 |

XXIX | 66 |

XXX | 68 |

XXXI | 70 |

XXXII | 74 |

XXXIV | 77 |

XXXV | 78 |

XXXVI | 79 |

XXXVII | 81 |

XXXVIII | 82 |

XXXIX | 84 |

XL | 85 |

XLI | 86 |

XLII | 88 |

XLIII | 91 |

XLIV | 92 |

XLV | 94 |

XLVI | 95 |

XLVII | 98 |

XLVIII | 99 |

XLIX | 101 |

L | 102 |

LI | 104 |

LII | 105 |

LIII | 106 |

LIV | 107 |

LV | 108 |

LVI | 109 |

LVII | 112 |

LVIII | 114 |

LIX | 115 |

LX | 120 |

LXI | 124 |

LXII | 126 |

LXIII | 127 |

LXV | 129 |

LXVI | 131 |

LXVII | 133 |

LXVIII | 135 |

LXIX | 136 |

LXXVIII | 153 |

LXXIX | 156 |

LXXX | 157 |

LXXXI | 159 |

LXXXII | 160 |

LXXXIII | 162 |

LXXXIV | 164 |

LXXXV | 165 |

LXXXVI | 167 |

LXXXVII | 169 |

LXXXVIII | 171 |

LXXXIX | 172 |

XC | 173 |

XCI | 174 |

XCII | 175 |

XCIII | 179 |

XCIV | 181 |

XCV | 183 |

XCVI | 184 |

XCVII | 186 |

XCVIII | 189 |

XCIX | 190 |

C | 191 |

CI | 193 |

CII | 195 |

CIII | 197 |

CIV | 198 |

CV | 199 |

CVII | 201 |

CVIII | 203 |

CIX | 204 |

CX | 206 |

CXI | 207 |

CXII | 208 |

CXIII | 209 |

CXIV | 211 |

CXV | 214 |

CXVI | 215 |

CXVII | 219 |

CXVIII | 220 |

CXIX | 221 |

CXX | 224 |

CXXI | 229 |

CXXII | 230 |

CXXIII | 232 |

CXXIV | 233 |

CXXV | 237 |

CXXVII | 239 |

CXXVIII | 240 |

CXXIX | 242 |

CXXX | 243 |

CXXXI | 245 |

CXXXII | 247 |

CXXXIII | 248 |

CXXXIV | 249 |

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### Common terms and phrases

algorithm Alice and Bob beam-splitter Bell binary bipartite Chapter classical communication classical information coherence complex computational basis consider copies correlated corresponding decoherence decomposition deﬁned deﬁnition density matrix described diﬀerent discussed down-conversion eﬀect eﬃciently eigenvalues elements encoded ensemble entanglement measures error correction example expectation values ﬁeld ﬁnd ﬁnite ﬁrst function given Hermitian hidden-variables Hilbert space inequality input interferometer linear LOCC matrix mixed multipartite multiple-qubit Neumann entropy number of bits orthogonal outcomes output pair particle Pauli performed photon Phys physical polarization postulate POVM probability problem projectors properties protocol provides pure quan quantity quantum channel quantum circuit quantum computation quantum gates quantum information processing quantum key distribution quantum mechanics quantum systems qubit result Sect Section single-qubit speciﬁc state-vectors statistical operator Stokes parameters subspace subsystems suﬃciently superposition theorem theory three-qubit tion Turing machine two-qubit unitary operation unitary transformations vector von Neumann entropy