## Principles of Quantum Computation And Information: Basic Tools And Special TopicsQuantum computation and information is a new, rapidly developing interdisciplinary field. Its fundamental concepts and central results may not be easily understood without facing numerous technical details. Building on the basic concepts introduced in Vol I, this second volume deals with various important aspects, both theoretical and experimental, of quantum computation and information in depth. The areas include quantum data compression, accessible information, entanglement concentration, limits to quantum computation due to decoherence, quantum error-correction, and the first experimental implementations of quantum information protocols. This volume also includes a selection of special topics: chaos and quantum to classical transition, quantum trajectories, quantum computation and quantum chaos, and the Zeno effect. |

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### Contents

Introduction 1 | 333 |

Introduction to Quantum Mechanics 49 | 257 |

Quantum Computation 99 | 334 |

Copyright | |

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Alice and Bob ancillary qubits assume atom basis billiards bit-flip Bloch sphere Bloch vector Bob's cavity channel chaotic classical CNOT gate codewords compression corresponding decoherence defined denotes density matrix density operator described distribution dynamical eigenstates eigenvalues electron encoding energy ensemble entanglement environment error correction error syndrome evolution Exercise experimental exponential field frequency given Hamiltonian Hermitian Hilbert space Holevo implement initial interaction ions Kraus operators large number laser Let us consider levels linear matrix elements means molecules motion Neumann entropy noise Note obtain orthogonal outcome parameters perturbation phase phase-flip photon polarization possible POVM probability protocol pulses pure quantum chaos quantum circuit quantum computation quantum gates quantum information quantum mechanics Rabi oscillations reduced density representation resonant rotation Schmidt decomposition sequence Shannon entropy shown in Fig single single-qubit spin statistical subspace subsystem superoperator superposition teleportation theorem three-qubit transition two-qubit unitary transformation wave function