Quantum search algorithms and quantum communication on networks

Quantum search algorithms - both for an ordered list and on an extended network - are based on propagating a well known initial quantum state into a localised target state. Grover's algorithm, one of the corner stones of modern quantum information theory, predicts a square root speed up of a search protocol based on wave mechanics compared to a ''classical'' search. I discuss extensions of Grover's ideas to searches on networks. I summarise the connections between quantum random walks, quantum searches and quantum graphs, and will offer a new interpretation of a quantum search in terms of avoided crossings and localised defect states. Setting up a communication channel between two parties is in fact closely related to a two-way search. Starting from this observation, it is shown that wave mechanics can be used to send signals efficiently between a sender and a receiver where neither party knows the address of the other. Possible experimental realisations are discussed.