Detecting Majorana fermions by nonlocal entanglement between quantum dots

Nonlocal entanglement between two quantum dots (QDs) can be generated through Majorana fermions. The two Majorana fermions at the ends of a one-dimensional topological superconductor form a nonlocal electronic level, which couples the occupation states of the two QDs located close to the two ends and brings the whole system into an entangled state, even at low temperatures and zero bias voltage. Upon introducing a charging energy by a capacitor, entanglement of the whole system can manifest itself through the nonlocal entanglement between the two QDs. Explicitly, the conditional probabilities of electron occupation on one QD with and without electron occupation on the other QD deviate from each other, with the difference proportional to the concurrence of quantum entanglement between the two QDs. Therefore detecting the difference in conditional probabilities, which is achievable experimentally by established techniques, provides evidence of the nonlocal nature of the fermion level constructed by the two end Majorana fermions.