Entanglement and quantum information theory in the context of higher dimensional spin systems.

摘要: Quantum information theory is an exciting, inter-disciplinary field, combining elements of condensed matter theory, quantum mechanics and theory. In this thesis, I shall make a modest contribution to field by examining entanglement in many-body systems with more than two levels. the first section, consider dynamics system qutrits three-level which are coupled through SU(3)-invariant permutation Hamiltonian. Each term Hamil- tonian nearest-neighbour operator, thus Hamiltonian may be considered generalisation standard SU (2)-invariant Heisenberg Hamiltonian, every (up addition identity operator) operator for two-level system. The has topology cross, (to limited extent) analogous beam-splitter. aim study establish Bell singlet state between distant parties. Building on work, go ground made up many-level same show that many levels systems. It high degree symmetry. will its application distribution measurements (localisable entanglement), discuss how it physically implemented ultracold atoms, Hubbard model. also famous valence bond solid (the Affleck-Kennedy- Lieb-Tasaki spin chain), all present extracted from single copy chain contrast gapless, critical chains, only half total extractable copy.