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Intro; Foreword; Preface; Structure of the Book; Acknowledgements; Contents; Part I Basic Concepts in Quantum Information Theory; 1 Correlation and Entanglement; 1.1 Introduction; 1.2 Correlations in Classical Probability Theory; 1.2.1 Joint Probability Without Correlations; 1.2.2 Correlation Functions; 1.2.3 Mutual Information; 1.3 Quantum Entanglement; 1.3.1 Pure and Mixed Quantum States; 1.3.2 Composite Quantum Systems and Tensor Product Structure; 1.3.3 Pure Bipartite State, Schmidt Decomposition; 1.3.4 Mixed Bipartite State; 1.3.5 Bell's Inequalities; 1.3.6 Entanglement
1.4 Correlation and Entanglement in Many-Body Quantum Systems1.4.1 The GHZ Paradox; 1.4.2 Many-Body Correlation; 1.4.3 Many-Body Entanglement; 1.5 Summary and Further Reading; References; 2 Evolution of Quantum Systems; 2.1 Introduction; 2.2 Unitary Evolution; 2.2.1 Single Qubit Unitary; 2.2.2 Two-Qubit Unitary; 2.2.3 N-Qubit Unitary; 2.3 Quantum Circuits; 2.4 Open Quantum Systems; 2.5 Master Equation; 2.5.1 The Lindblad Form; 2.5.2 Master Equations for a Single Qubit; 2.6 Summary and Further Reading; References; 3 Quantum Error-Correcting Codes; 3.1 Introduction
3.2 Basic Idea of Error Correction3.2.1 Bit Flip Code; 3.2.2 Shor's Code; 3.2.3 Other Noise Models; 3.3 Quantum Error-Correcting Criteria, Code Distance; 3.4 The Stabilizer Formalism; 3.4.1 Shor's Code; 3.4.2 The Stabilizer Formalism; 3.4.3 Stabilizer States and Graph States; 3.5 Toric Code; 3.6 Summary and Further Reading; References; Part II Local Hamiltonians, Ground States, and Many-Body Entanglement; 4 Local Hamiltonians and Ground States; 4.1 Introduction; 4.2 Many-Body Hilbert Space; 4.3 Local Hamiltonians; 4.3.1 Examples; 4.3.2 The Effect of Locality
4.4 Ground-State Energy of Local Hamiltonians4.4.1 The Local Hamiltonian Problem; 4.4.2 The Quantum Marginal Problem; 4.4.3 The N-Representability Problem; 4.4.4 de Finetti Theorem and Mean-Field Bosonic Systems; 4.5 Frustration-Free Hamiltonians; 4.5.1 Examples of Frustration-Free Hamiltonians; 4.5.2 The Frustration-Free Hamiltonians Problem; 4.5.3 The 2-Local Frustration-Free Hamiltonians; 4.6 Summary and Further Reading; References; 5 Gapped Quantum Systems and Entanglement Area Law; 5.1 Introduction; 5.2 Quantum Many-Body Systems; 5.2.1 Dimensionality and Locality
1.4 Correlation and Entanglement in Many-Body Quantum Systems1.4.1 The GHZ Paradox; 1.4.2 Many-Body Correlation; 1.4.3 Many-Body Entanglement; 1.5 Summary and Further Reading; References; 2 Evolution of Quantum Systems; 2.1 Introduction; 2.2 Unitary Evolution; 2.2.1 Single Qubit Unitary; 2.2.2 Two-Qubit Unitary; 2.2.3 N-Qubit Unitary; 2.3 Quantum Circuits; 2.4 Open Quantum Systems; 2.5 Master Equation; 2.5.1 The Lindblad Form; 2.5.2 Master Equations for a Single Qubit; 2.6 Summary and Further Reading; References; 3 Quantum Error-Correcting Codes; 3.1 Introduction
3.2 Basic Idea of Error Correction3.2.1 Bit Flip Code; 3.2.2 Shor's Code; 3.2.3 Other Noise Models; 3.3 Quantum Error-Correcting Criteria, Code Distance; 3.4 The Stabilizer Formalism; 3.4.1 Shor's Code; 3.4.2 The Stabilizer Formalism; 3.4.3 Stabilizer States and Graph States; 3.5 Toric Code; 3.6 Summary and Further Reading; References; Part II Local Hamiltonians, Ground States, and Many-Body Entanglement; 4 Local Hamiltonians and Ground States; 4.1 Introduction; 4.2 Many-Body Hilbert Space; 4.3 Local Hamiltonians; 4.3.1 Examples; 4.3.2 The Effect of Locality
4.4 Ground-State Energy of Local Hamiltonians4.4.1 The Local Hamiltonian Problem; 4.4.2 The Quantum Marginal Problem; 4.4.3 The N-Representability Problem; 4.4.4 de Finetti Theorem and Mean-Field Bosonic Systems; 4.5 Frustration-Free Hamiltonians; 4.5.1 Examples of Frustration-Free Hamiltonians; 4.5.2 The Frustration-Free Hamiltonians Problem; 4.5.3 The 2-Local Frustration-Free Hamiltonians; 4.6 Summary and Further Reading; References; 5 Gapped Quantum Systems and Entanglement Area Law; 5.1 Introduction; 5.2 Quantum Many-Body Systems; 5.2.1 Dimensionality and Locality