Stochastic quantum teleportation and entanglement distillation with imperfect cluster states

Cluster states form a class of non-separable multipartite graph states, the entanglement of which is exceptionally persistent against the effects of single-qubit measurements. Quantum teleportation between the qubits within a cluster state constitutes the basic operation in a new approach to universal quantum computing, known as one-way quantum computing. One of the most promising experimental approaches to one-way quantum computing employs ultracold atoms in optical lattices, allowing cluster states of various sizes, geometries, and dimensions, to be generated with superior efficiency. In practice, systematic phase errors are expected to arise during the entangling process, resulting in the formation of imperfect cluster states. A technique for performing quantum teleportation in the presence of systematic phase errors is presented in this thesis, and allows maximally entangled GHZ states to be distilled from imperfect cluster states. Applications include fault-tolerant quantum computing, open-destination quantum teleportation, quantum cryptography, Heisenberg-limited spectroscopy, and atomic clocks.