QUANTUM INFORMATION PROCESSING : theory and implementation.

Description

Preface to the Second Edition Preface Contents 1 Introduction 1.1 The Qubit 1.2 Quantum Gates 1.3 Quantum Circuits 1.4 The Deutsch Algorithm 1.5 An Interferometer Version 1.6 Other Models of Quantum Computation 1.7 Discussion 1.8 Problems Further Reading 2 The Density Matrix 2.1 Ensembles and Subsystems 2.2 Properties 2.3 Pure States and Mixed States of a Qubit 2.4 Pure State Decompositions and the Ensemble Interpretation 2.5 A Mathematical Aside: The Schmidt Decomposition of a Bipartite State 2.6 Purfication, Reduced Density Matrices and the Subsystem Interpretation 2.7 Comparing Density Matices 2.8 Problems Further Reading 3 Entanglement 3.1 Definition of Entanglement 3.2 Faster Than Light Communication 1 3.3 Bell Inequalities 3.4 Representative Applications of Entanglement: Dense Coding, Teleportation and Entanglement Swapping 3.4.1 Dense Coding 3.4.2 Teleportation 3.4.3 Entanglement Swapping 3.5 Conditions of Separability 3.6 Entanglement Distillation and Formation 3.6.1 Local Operations and Classical Communication [LOCC] 3.6.2 Entanglement Distillation: Procrustean Method 3.6.3 Entanglement Formation 3.7 Entanglement Measures 3.7.1 The von Neumann Entropy as an Entanglement Measure for Pure Bipartite States: A First Set of Properties 3.7.2 A Useful Auxiliary Quantity: Relative Entropy and Klein's Inequality 3.7.3 The von Neumann Entropy: A Second Set of Properties 3.7.4 The Effect of Local Measurements on Entanglement 3.7.5 Towards the Entanglement of Mixed States 3.7.6 The Effect of Throwing Away Part of the System Locally on Entanglement 3.7.7 Bound Entanglement 3.8 Concurrence and Negativity 3.9 Multipartite Entanglement 3.10 Problems Further Reading 4 Generalized Quantum Dynamics 4.1 Quantum Maps or Superoperators 4.1.1 Quantum Maps and Their Kraus Representation 4.1.2 Properties of Quantum Maps 4.1.3 Properties of the Kraus Operators 4.2 An Example: The Depolarizing Channel 4.3 An Impossible Map 4.3.1 The Cloning Map and the No-Cloning Theorem 4.3.2 Faster Than Light Communication II 4.4 Problems Further Reading 5 Quantum Measurement Theory 5.1 Outline 5.2 Standard Quantum Measurements 5.3 Positive Operator Valued Measures: POVM's 5.4 Neumark's Theorem and the Implementation of a POVM via Generalized Measurements 5.5 Examples: Strategies for State Discrimination 5.5.1 Unambiguous Discrimination of Two Pure States 5.5.2 Minimum Error Discrimination of Two Quantum States 5.6 Sequential Measurements 5.6.1 Simple Example 5.6.2 Sequential Unambiguous Discrimination 5.7 Problems Further Reading 6 Quantum Cryptography 6.1 Outline 6.2 The One Time Pad 6.3 The B92 Quantum Key Distribution Protocol 6.4 The BB 84 Protocol 6.5 The E91 Protocol and Device-Independent Key Distribution 6.6 Quantum Secret Sharing 6.7 Problems Further Reading 7 Quantum Algorithms 7.1 The Deutsch-Jozsa Algorithm 7.2 The Bernstein-Vazirani Algorithm 7.3 Quantum Search: The Grover Algorithm 7.4 Period Finding: Simon's Algorithm 7.5 Quantum Fourier Transform and Phase Estimation 7.6 Quantum Walks 7.7 Quantum Simulation 7.8 QAOA 7.9 Problems Further Reading 8 Quantum Machines 8.1 Introduction 8.2 Cloners and U-NOT Gates 8.3 Programmable Machines: A General Result 8.4 Probabilistic Processors 8.5 A Programmable State Discriminator 8.6 Problems Further Reading 9 Decoherence and Quantum Error Correction 9.1 General Theory of Quantum Error-Correcting Codes 9.2 An Example: CSS Codes 9.3 Decoherence-Free Subspaces 9.4 Problems Further Reading 10 The Stabilizer Formalism and the Gottesman–Knill Theorem 10.1 Stabilizer Formalism 10.2 Description of Gates and Measurements 10.3 The Gottesman–Knill Theorem 10.4 Proof of Theorem 2 10.5 Problems Further Reading 11 Quantum Information Theory 11.1 Comparing Classical Probability Distributions 11.2 Comparing Quantum States 11.3 Entropies for Two Classical Random Variables 11.4 Quantum Properties 11.5 The Holevo Theorem 11.6 Example: Unambiguous Discrimination 11.7 Problems Further Reading 12 Implementations 12.1 DiVincenzo Criteria 12.2 Quantum Dynamics 12.3 Bloch Equations and Qubit Coherence 12.4 Rabi Oscillations 12.4.1 One-Qubit Gates 12.4.2 Composite Pulses 12.5 Ramsey Interferometry and a Qubit in a Noisy Environment 12.5.1 Dynamical Decoupling 12.6 Problems References 13 Atomic Qubits 13.1 Neutral Atoms 13.2 Laser Cooling and Trapping 13.3 Qubit State Preparation, Measurement, and Coherence 13.4 One-Qubit Gates 13.5 Two-Qubit Gates 13.6 Trapped Ions 13.7 Ion Traps 13.7.1 Multiple Ions 13.8 Coupling of Electronic and Motional Degrees of Freedom 13.9 Two-Qubit Gates 13.9.1 Cirac–Zoller Gate 13.9.2 Mølmer–Sørensen Gate 13.10 Status and Outlook 13.11 Problems References 14 Optical Qubits 14.1 Photons and Beamsplitters 14.2 Probabilistic CNOT Gate 14.3 Gate Teleportation 14.4 Nonlinear Optical Approaches 14.4.1 Single Photon Nonlinearities 14.4.2 Continuous Variable Encoding 14.5 Problems References 15 Solid State Qubits 15.1 Superconducting Qubits: Overview 15.2 Circuit Quantization 15.3 Superconductivity 15.4 Flux Quantization 15.5 Josephson Junction 15.6 Qubit Designs 15.6.1 Charge Qubit 15.6.2 Flux Qubit 15.6.3 Phase Qubit 15.7 Transmon 15.8 Coupling Qubits to Resonators 15.9 Protected Qubits 15.10 Outlook 15.11 Quantum Dot Qubits: Overview 15.12 State Preparation and Measurement 15.13 One-Qubit Gates 15.14 Two-Qubit Gates 15.15 Variations on a Theme 15.16 Outlook 15.17 Problems References Index