Entanglement and its applications in systems with many degrees of freedom

Abstract

Entanglement are the non-local correlations permitted by quantum theory, believed to play a fundamental role in a quantum computer. We have investigated these correlations in a number of theoretical models for condensed matter systems. Such systems are likely candidates for quantum computing, and experimentally feasible for instance as superconducting qubits. At quantum critical points the ground state of these systems is very complicated, and the entanglement is usually larger than at non-critical points. This entanglement can be used to identify the critical points through what we denote the entanglement signature, even for very small systems. From another perspective, it seems that the entanglement is an essential tool to find an unknown ground state, since this gives rise to a simple decomposition of the state.

arXiv commentPhD thesis, 85 pages

References in corpus (41)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• A computable measure of entanglement
• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• Entanglement of a Pair of Quantum Bits
• Entanglement in quantum critical phenomena
• Efficient classical simulation of slightly entangled quantum computations
• Quantifying Entanglement
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
• Entanglement renormalization
• On Geometric Entropy
• Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model
• Criticality, the area law, and the computational power of PEPS
• Entanglement in the Quantum Heisenberg XY model
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Applied Conformal Field Theory
• "Squashed Entanglement" - An Additive Entanglement Measure
• Universality of Entropy Scaling in 1D Gap-less Models
• Limits for entanglement measures
• Entanglement of formation for symmetric Gaussian states
• General criterion for the entanglement of two indistinguishable particles
• Distillability Criterion for all Bipartite Gaussian States
• Separability Criterion for all bipartite Gaussian States
• Gaussian Entanglement of Formation
• Global entanglement and quantum criticality in spin chains
• Quantum search without entanglement
• The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography
• Fine-grained entanglement loss along renormalization group flows
• Single-copy entanglement in critical spin chains
• Theory of d-density wave viewed from a vertex model and its implications
• Entropy and Exact Matrix Product Representation of the Laughlin Wave Function
• Resonating plaquette phase of a quantum six-vertex model
• Entanglement in bosonic systems
• Entanglement properties of quantum spin chains
• Entanglement used to identify critical systems
• Thermalization through unitary evolution of pure states
• Measures of entanglement in quantum mechanics
• Quantum correlations in (1+1)-dimensional systems