Bell's inequality and universal quantum gates in a cold atom chiral fermionic p-wave superfluid

We propose and analyze a probabilistic scheme to entangle two spatially separated topological qubits in a $p_{x}+ip_{y}$ superfluid using controlled collisions between atoms in movable dipole traps and unpaired atoms inside vortex cores in the superfluid. We discuss how to test the violation of Bell's inequality with the generated entanglement. A set of universal quantum gates is shown to be implementable \textit{deterministically} using the entanglement despite the fact that the entangled states can only be created probabilistically.