Testable signatures of quantum non-locality in a two-dimensional chiral p-wave superconductor

A class of topological excitations -- the odd-winding number vortices -- in a spinless 2D chiral p-wave (p_x+ip_y) superconductor trap Majorana fermion states in the vortex cores. For a dilute gas of such vortices, low-energy \textit{fermionic} eigenstates have amplitudes $\sim\mathcal{O} (1)$ only near the vortex cores and exponentially small in between, hence are intrinsically non-local. We predict two testable signatures of this unusual quantum non-locality in quasiparticle tunneling experiments. We discuss why the associated teleportation-like phenomenon does not imply the violation of causality.