Effects associated with the existence of isolated zero modes of Majorana fermions are discussed. It is argued that the quantization of this system necessarily contains highly extended (stretched) quantum states and that, populating or depopulating such states by interacting with the quantum system, leads to long- ranged teleportation-like processes. A model consisting of a quantum wire embedded in a p-wave superconductor is discussed as an explicit - and exactly solvable- example of a physical system with isolated Majorana zero modes.