Non-local quantum phenomena associated with the Majorana fermion bound states in a $p_x+ip_y$ superconductor

We consider two quantum dots in tunneling contact with two vortices of a $p_x+ip_y$ superconductor. Due to the unusual zero energy fermion eigenstate formed by the linear combination of the Majorana fermion states localized in each vortex core, there are interesting non-local phenomena. Examples include teleportation of the amplitude of a quasiparticle, and the non-local effect of biasing one quantum dot on the tunneling curve of the other. We discuss why the teleportation of the amplitude does not imply the violation of causality.