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Supervisor's Foreword; Acknowledgments; Contents; 1 Introduction; 1.1 One-Way Quantum Computation; 1.1.1 Quantum Computation; 1.1.2 Quantum Teleportation; 1.1.3 Application of Quantum Teleportation to Quantum Computation (Gate Teleportation, Offline Scheme); 1.1.4 Application of Quantum Teleportation to Quantum Computation (One-Way Quantum Computation); 1.1.5 Circuit Model and Cluster Model; 1.1.6 Continuous-Variables and Universality; 1.2 History of One-Way Quantum Computation and This Thesis; 1.2.1 History of One-Way Quantum Computation; 1.2.2 This Thesis; 1.3 Structure of This Thesis.
3.2.6 Expectation Value and Covariance Matrix of Quadrature Operators3.2.7 Wigner Function and Gaussian State; 3.2.8 Quadrature Operator Which Specifies a Particular Quantum State; 3.3 Representations of Quantum State Manipulations; 3.3.1 Unitary Operator, Transformation of State Vector, Schrödinger Picture; 3.3.2 Transformation of Density Operator; 3.3.3 Transformation of Stabilizer; 3.3.4 Transformation of Nullifier; 3.3.5 Transformation of Annihilation Operator, Heisenberg Picture; 3.3.6 Transformation of Expectation Values and Covariance Matrix for Gaussian Operations.
3.3.7 Comparison Between Transformation of Nullifier and Transformation of Annihilation Operator3.3.8 Transformation of Quadrature Operator Which Specifies a Particular Quantum State; 3.4 Group of Operator; 3.4.1 Pauli Group (Heisenberg-Weyl Group); 3.4.2 Symplectic Group; 3.4.3 Clifford Group (Gaussian Operation); 3.4.4 Gaussian Operation as Clifford Group; 3.4.5 Summary of Names; 3.5 Operators; 3.5.1 Position Displacement Operator; 3.5.2 Momentum Displacement Operator; 3.5.3 Rotation Operator; 3.5.4 Fourier Operator; 3.5.5 Quadratic Phase Operator; 3.5.6 Two-Mode Interaction Operator.
3.5.7 Controlled-Z Operator3.5.8 Beam Splitter Operator; 3.6 Universality and Classical Simulation; 3.6.1 Universality; 3.6.2 Efficient Classical Simulation; 3.7 Entangled States and Entanglement Criteria; 3.7.1 Entangled States; 3.7.2 Entanglement Criteria; 3.7.3 Duan Criterion; 3.7.4 Extension of van Loock-Furusawa Criterion; 3.7.5 Entanglement Criteria via Partial Transpose of Density Operators; 3.7.6 Logarithmic Negativity; 3.7.7 Comparison of Entanglement Criteria; References; 4 Offline Scheme and One-Way Quantum Computation; 4.1 Quantum Teleportation and Gate Teleportation.
3.2.6 Expectation Value and Covariance Matrix of Quadrature Operators3.2.7 Wigner Function and Gaussian State; 3.2.8 Quadrature Operator Which Specifies a Particular Quantum State; 3.3 Representations of Quantum State Manipulations; 3.3.1 Unitary Operator, Transformation of State Vector, Schrödinger Picture; 3.3.2 Transformation of Density Operator; 3.3.3 Transformation of Stabilizer; 3.3.4 Transformation of Nullifier; 3.3.5 Transformation of Annihilation Operator, Heisenberg Picture; 3.3.6 Transformation of Expectation Values and Covariance Matrix for Gaussian Operations.
3.3.7 Comparison Between Transformation of Nullifier and Transformation of Annihilation Operator3.3.8 Transformation of Quadrature Operator Which Specifies a Particular Quantum State; 3.4 Group of Operator; 3.4.1 Pauli Group (Heisenberg-Weyl Group); 3.4.2 Symplectic Group; 3.4.3 Clifford Group (Gaussian Operation); 3.4.4 Gaussian Operation as Clifford Group; 3.4.5 Summary of Names; 3.5 Operators; 3.5.1 Position Displacement Operator; 3.5.2 Momentum Displacement Operator; 3.5.3 Rotation Operator; 3.5.4 Fourier Operator; 3.5.5 Quadratic Phase Operator; 3.5.6 Two-Mode Interaction Operator.
3.5.7 Controlled-Z Operator3.5.8 Beam Splitter Operator; 3.6 Universality and Classical Simulation; 3.6.1 Universality; 3.6.2 Efficient Classical Simulation; 3.7 Entangled States and Entanglement Criteria; 3.7.1 Entangled States; 3.7.2 Entanglement Criteria; 3.7.3 Duan Criterion; 3.7.4 Extension of van Loock-Furusawa Criterion; 3.7.5 Entanglement Criteria via Partial Transpose of Density Operators; 3.7.6 Logarithmic Negativity; 3.7.7 Comparison of Entanglement Criteria; References; 4 Offline Scheme and One-Way Quantum Computation; 4.1 Quantum Teleportation and Gate Teleportation.