## 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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Alice and Bob amplitude-damping ancillary qubits assume atom basis billiards bit-flip Bloch sphere Bloch vector chaotic classical CNOT gate compression corresponding decoherence decomposition defined denotes density matrix density operator described diagonal distribution dynamical chaos eigenstates eigenvalues encoding energy ensemble environment errors evolution Exercise fidelity decay follows frequency given Hamiltonian Hermitian Hilbert space initial interaction ions Kraus operators Kraus representation large number laser Let us consider letters levels Lyapunov master equation matrix elements means motion Neumann entropy noise channel Note obtain orthogonal oscillations outcome parameters perturbation phase photon possible POVM probability pulses pure quantum chaos quantum circuit quantum circuit implementing quantum computation quantum gates quantum information quantum mechanics quantum system qubit random Schmidt decomposition sequence Shannon entropy shown in Fig single-qubit spin statistical subspace subsystem superoperator superposition teleportation theorem trajectories transition two-qubit von Neumann entropy wave function