| Description |
1 online resource (362 p.) |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgments -- Preface to the Second Edition -- List of Problems -- SECTION I: Preliminaries -- Chapter 1: Introduction -- 1.1. What is this book about? -- 1.1.1. Synopsis -- 1.2. How to use this book -- 1.3. Mathematical notation, conventions and basic formulae -- 1.3.1. Hilbert spaces and operators -- 1.3.2. Linear algebra and direct sums -- 1.3.2.1. Singular Value Decomposition -- 1.3.2.2. Schur Complements -- 1.3.3. Compact outer product notation -- 1.3.4. Delta functions -- 1.3.5. Gaussian integrals |
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1.3.6. Miscellanea -- Chapter 2: Quantum Mechanics: Instructions for Use -- 2.1. Quantum states and quantum measurements -- 2.2. CP-maps and unitary transformations -- 2.3. Dynamics: Hamiltonians and master equations -- 2.4. Continuous variables -- 2.5. Entropies -- 2.6. Quantum entanglement -- 2.6.1. Entanglement of pure quantum states -- 2.6.2. Partial transposition and logarithmic negativity -- 2.7. Further reading -- SECTION II: Foundations -- Chapter 3: Gaussian States of Continuous Variable Systems -- 3.1. Canonical commutation relations -- 3.2. Quadratic Hamiltonians and Gaussian states |
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3.2.1. Displacement operators -- 3.2.2. The symplectic group of linear canonical transformations -- 3.2.3. Normal modes -- 3.2.4. Normal mode decomposition of a Gaussian state -- 3.2.5. The Fock basis -- 3.3. Statistical moments of a Gaussian state and the covariance matrix -- 3.4. The uncertainty principle -- 3.5. Purity and entropies of Gaussian states -- 3.6. Further reading -- Chapter 4: Phase Space Methods -- 4.1. Coherent states -- 4.2. The Fourier-Weyl relation -- 4.3. Characteristic functions and quasi-probability distributions -- 4.3.1. General properties of the characteristic function |
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4.3.2. Quasi-probability distributions -- 4.4. Characteristic function of a Gaussian state -- 4.5. Further reading -- SECTION III: Dynamics -- Chapter 5: Gaussian Operations -- 5.1. Gaussian unitary transformations -- 5.1.1. Linear displacements -- 5.1.2. Symplectic transformations -- 5.1.2.1. Passive Transformations: Phase Shifters and Beam Splitters -- 5.1.2.2. Squeezing Transformations -- 5.2. Tensor products and partial traces of Gaussian states -- 5.3. Deterministic Gaussian CP-maps -- 5.3.1. Dual Gaussian CP-maps and action onWeyl operators -- 5.3.2. Classical mixing |
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5.3.3. Losses, attenuators and amplifiers -- 5.4. Gaussian measurements -- 5.4.1. Homodyne detection -- 5.4.1.1. Homodyne Generating Function -- 5.4.2. Bell measurements and heterodyne detection -- 5.4.3. Ideal general-dyne detections -- 5.4.4. Noisy measurements -- 5.4.5. Conditional Gaussian dynamics -- 5.5. Choi-Jamiolkowski description of the most general Gaussian CP-map -- 5.5.1. Choi isomorphism and gate teleportation -- 5.5.2. Choi isomorphism in infinite dimension -- 5.5.3. The most general Gaussian CP-map -- 5.6. Further reading -- Chapter 6: Diffusive Dynamics and Continuous Monitoring |
| Notes |
Description based upon print version of record |
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6.1. Linear and quadratic Hamiltonian dynamics |
| Subject |
Quantum computing.
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Quantum computing
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| Form |
Electronic book
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| ISBN |
9781000920505 |
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100092050X |
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