Wave Communication across Regular Lattices

We propose a novel way to communicate signals in the form of waves across a d-dimensional lattice. The mechanism is based on quantum search algorithms and makes it possible to both search for marked positions in a regular grid and to communicate between two (or more) points on the lattice. Remarkably, neither the sender nor the receiver needs to know the position of each other despite the fact that the signal is only exchanged between the contributing parties. This is an example of using wave interference as a resource by controlling localization phenomena effectively. Possible experimental realizations will be discussed.