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Umfang: 1 online resource (549 pages)

ISBN: 3-031-03998-X

Serie: Quantum Science and Technology

Anmerkung: Includes index. , Intro -- Preface -- References -- Contents -- Editors and Contributors -- About the Editors -- Contributors -- Entanglement Spectra of Spin Chains -- 1 Entanglement Spectra of Many-Body Ground States -- 2 Decomposition of Spin Chain Hilbert Spaces -- 3 Gapped Spin Chains -- 4 Gapless Spin Chains -- 5 Conclusion -- References -- Detecting Quantum Phase Transitions in Spin Chains -- 1 Introduction to Quantum Entanglement -- 1.1 Quantum Entanglement and Quantum Phase Transitions -- 1.2 Methodologies from the Viewpoint of Quantum Information Theory -- 1.3 Open Questions -- 2 Concurrence and Quantum Phase Transitions in Spin Chains -- 3 von Neumann Entropy and Quantum Phase Transitions -- 3.1 Single-Site Entanglement -- 3.2 Multisite Entanglement -- 3.3 Entanglement and Quantum Phase Transitions at Finite Temperatures -- 3.4 Entanglement and Quantum Correlations -- 4 Quantum Discord, Quantum Coherence, and Quantum Phase Transitions -- 4.1 Quantum Discord -- 4.2 Quantum Coherence and Quantum Coherence Spectrum -- 5 Deducing Order Parameters from Entanglement Based Method -- 6 Summary and Outlook -- References -- Entanglement Entropy in Critical Quantum Spin Chains with Boundaries and Defects -- 1 Introduction -- 2 Entanglement Entropy in CFTs with Boundaries -- 2.1 Ising Model -- 2.2 The Free, Compactified Boson Model -- 3 Entanglement Entropy in CFTs with Defects -- 3.1 The Ising Model -- 3.1.1 Energy Defect -- 3.1.2 Duality Defect -- 3.2 The Free, Compactified Boson Model -- 4 Conclusion -- References -- Entanglement Entropy and Localization in Disordered QuantumChains -- 1 Introduction -- 1.1 Generalities -- 1.2 Random Spin Chain Models -- 1.2.1 Disordered XXZ Hamiltonians -- 1.2.2 Random Transverse Field Ising Chains -- 1.2.3 Many-Body Localization -- 1.3 Chapter Organization -- 2 Entanglement in Non-interacting Anderson Localized Chains. , 2.1 Disordered XX Chains and Single-Particle Localization Lengths -- 2.1.1 Localization Length from the Participation Ratio (PR) -- 2.1.2 Numerical Results for the Localization Lengths -- 2.2 Entanglement Entropy for Many-Body (Anderson Localized) Eigenstates -- 2.2.1 Free-Fermion Entanglement Entropy -- 2.2.2 Low and High Energy -- 2.2.3 Strong Disorder Limit -- 3 Entanglement and Infinite Randomness Criticalities -- 3.1 Entanglement in Disordered XXZ and Quantum Ising Chains -- 3.1.1 Random Singlet State for Disordered S=1/2 Chains -- 3.1.2 Infinite Randomness Criticality at High Energy -- 3.2 Other Systems Showing Infinite Randomness Criticality -- 3.2.1 Higher Spins, Golden Chain, and RG Flows -- 3.2.2 d> -- 1 Infinite Randomness -- 3.3 Engineered Disorders -- 4 Many-Body Localization Probed by Quantum Entanglement -- 4.1 Area vs. Volume-Law Entanglement for High-Energy Eigenstates -- 4.2 Distributions of Entanglement Entropies -- 4.2.1 Distribution Across the ETH-MBL Transition -- 4.2.2 Strong Disorder Distributions -- 5 Concluding Remarks -- References -- Some Aspects of Affleck-Kennedy-Lieb-Tasaki Models: Tensor Network, Physical Properties, Spectral Gap, Deformation, and Quantum Computation -- 1 Introduction -- 2 Tensor-Network Picture: MPS and PEPS -- 2.1 1D AKLT Chain -- 2.2 Two Dimensions -- 2.2.1 Honeycomb/Hexagonal Lattice -- 2.2.2 Square Lattice -- 2.3 Boundary Conditions and Degeneracy of AKLT Models -- 3 Magnetic Ordering -- 4 Symmetry-Protected Topological Order -- 4.1 SPT Order of 1D AKLT State -- 4.2 Two Dimensions: Honeycomb and Square Lattices -- 5 Hidden Order in AKLT States -- 5.1 String Order Parameter -- 5.2 Hidden Cluster Order -- 5.3 Hidden Frustration on Frustrated Lattices -- 6 Applications in Quantum Computation -- 6.1 One Dimension -- 6.1.1 Logical Identity and One-Qubit Gates. , 6.1.2 Reduction to the 1D Cluster State -- 6.2 Two Dimensions: Universal Computation -- 7 Spectral Gap for AKLT Models -- 8 Deformed AKLT Models and Phase Transitions -- 8.1 1D Deformed AKLT Chain -- 8.2 2D Deformed AKLT Models and Their Phase Transitions -- 9 Conclusion -- References -- Machine Learning-Assisted Entanglement Measurement in Quantum Many-Body Systems -- 1 Introduction -- 2 PPT Criterion and Entanglement Measurement -- 2.1 Werner States -- 3 Measuring the PT Moments -- 3.1 Measurement in Spin Systems -- 3.2 Measurement in Bosonic Systems -- 4 Neural Network Entanglement Estimator -- 4.1 Choice of the Training Set -- 4.2 Sensitivity and Error Analysis -- 4.3 Comparison with Approximate State Reconstruction Methods -- 5 Numerical Results -- 5.1 Ground States Through a Quantum Phase Transition -- 5.2 Quench Across a Phase Transition -- 5.3 W-State -- 6 Conclusions -- References -- Local Convertibility in Quantum Spin Systems -- 1 The Cluster-Ising Model -- 2 The λ-D Model -- 3 The Perturbed Toric Code -- 4 The Quantum Ising Chain -- 4.1 The Rényi Entropies -- 4.2 The Correlation Matrix -- 4.3 The Z2 Symmetric Ground State -- 4.4 Symmetry Broken Ground State -- 5 Origin of SSB -- 5.1 Two-Body Quantum Correlations -- 5.2 Global Properties: Local Convertibility and Many-Body Entanglement Sharing -- 5.3 Many-Body Entanglement Distribution -- 6 Conclusions -- Bibliography -- Optimal Parent Hamiltonians for Many-Body States -- 1 Introduction -- 2 The Space of Symmetries -- 3 From Ground States to Parent Hamiltonians -- 4 The Time-Dependent Inverse Problem -- 5 Conclusions -- References -- Entanglement Dynamics in Hybrid Quantum Circuits -- 1 Introduction -- 2 Random Unitary Quantum Circuits -- 2.1 Entanglement Growth -- 2.1.1 Mapping to KPZ Dynamics of Random Surface Growth -- 2.1.2 Directed Polymer and Minimal-Cut Interpretation. , 2.2 Operator Spreading -- 2.3 U(1) Symmetric Circuits -- 3 Measurement-Induced Phase Transitions -- 3.1 Entanglement Transition -- 3.2 Alternative Perspectives on MIPTs -- 3.2.1 Purification Transition -- 3.2.2 Ancilla Probe of Purification Transition -- 3.2.3 Experimental Observation of MIPT in Trapped Ions -- 3.2.4 Connection to Quantum Channel Capacity and Quantum Error Correction -- 3.2.5 Information Gained by the Observer -- 4 Replica Statistical Mechanics Models -- 4.1 Replica Trick -- 4.2 Haar Calculus and Boltzmann Weights -- 4.3 Boundary Conditions and Domain Wall Free Energy -- 4.4 Symmetry and Conformal Invariance -- 4.5 Large Hilbert Space Dimension Limit -- 4.5.1 Mapping Onto Classical Percolation -- 4.5.2 Entanglement and Minimal-Cut Picture -- 4.6 Finite d Universality Class -- 5 Symmetry and Topology in Measurement-Induced Phases and Criticality -- 5.1 Symmetric Monitored Random Circuits -- 5.2 Area-Law Phases -- 5.2.1 Measurement-Induced Symmetry-Breaking Order in 1+1d -- 5.2.2 Measurement-Induced Topological Orders -- 5.3 Volume-Law Phases -- 5.3.1 Volume-Law Phases with Order-Stat-Mech Perspective -- 5.3.2 Charge Sharpening Transitions in the Volume-Law Phase -- 6 Discussion -- References -- Quantum Simulation Using Noisy Unitary Circuits and Measurements -- 1 Introduction -- 2 Measurement-Induced Entanglement Transitions in Hybrid Quantum Circuits -- 2.1 Quantum Trajectories -- 2.2 Monitored Quantum Circuits -- 2.3 Purification Transition -- 2.4 Transitions in the Rényi Entropies -- 2.5 Analytically Tractable Limits -- 2.6 Critical Properties of Measurement-Induced Transitions -- 2.7 Entanglement Transitions in Experiments -- 2.7.1 Scalability Issues -- 2.7.2 Measurement-Induced Transition in a Trapped-Ion Experiment -- 3 Random Circuits on Noisy-Intermediate Scale Quantum Devices. , 3.1 Random-Circuit Sampling for Achieving a Quantum Computational Advantage -- 3.2 Applications of Random Circuits in Quantum Many-Body Physics -- 4 Conclusion -- References -- Entanglement Dynamics in Spin Chains with Structured Long-Range Interactions -- 1 Introduction -- 2 Quantifying Entanglement and Information Spreading -- 2.1 Measures of Entanglement Entropy -- 2.2 Lieb-Robinson Bounds and OTOCs -- 2.3 Quasiparticle Approaches -- 2.4 Matrix Product States (MPS) -- 3 Power-Law Interacting Models -- 3.1 Short-Range Regime, α> -- 2 -- 3.2 Intermediate Range Regime, 1 < -- α< -- 2 -- 3.3 Long-Range Regime, α< -- 1 -- 4 Fast Scrambling and Sparse Models -- 4.1 Sparse Nonlocal Interactions for Fast Scrambling -- 4.2 Sparse Nonlocal Fast Scramblers -- 5 Implementation in Experiments -- 5.1 Long-Range Interactions with Trapped Ions -- 5.2 Long-Range Interactions with Rydberg Atoms -- 5.3 Long-Range Interactions in Cavity Quantum Electrodynamics -- 6 Outlook and Further Connections -- References -- Quantum Map Approach to Entanglement Transfer and Generation in Spin Chains -- 1 Introduction -- 2 Quantum Dynamical Maps -- 3 U(1)-Symmetric Hamiltonians -- 4 One-Qubit Map -- 5 Two-Qubit Map -- 6 Two-Qubit Entanglement Generation -- 7 Four-Qubit Entanglement Generation -- 8 Conclusion -- References -- Weak Ergodicity Breaking Through the Lens of QuantumEntanglement -- 1 Introduction -- 2 Matrix Product State Methods -- 2.1 Towers of Quasiparticles -- 2.2 Time-Dependent Variational Principle -- 3 Mechanisms of Weak Ergodicity Breaking -- 3.1 Spectrum Generating Algebra -- 3.2 Hilbert Space Fragmentation -- 3.3 Projector Embedding -- 4 PXP Model -- 4.1 The Model -- 4.2 Ergodicity Breaking in the PXP Model -- 4.3 The Origin of Non-thermal Eigenstates and Quantum Revivals -- 5 Semiclassical Dynamics -- 5.1 Discussion: Benefits and Pitfalls of TDVP. , 6 Quantum Many-Body Scars.

Weitere Ausg.: ISBN 3-031-03997-1

Sprache: Englisch