Splitting of a Cooper Pair by a Pair of Majorana Bound States

We propose a method to probe the nonlocality of a pair of Majorana bound states by crossed Andreev reflection, which is the injection of an electron into one bound state followed by the emission of a hole by the other (equivalent to the splitting of a Cooper pair). We find that, at sufficiently low excitation energies, this nonlocal scattering process dominates over local Andreev reflection involving a single bound state. As a consequence, the low-temperature and low-frequency fluctuations $\delta I_i$ of currents into the two bound states $i=1$, 2 are maximally correlated: $\overline{\delta I_1\delta I_2}=\overline{\delta I_i^2}$.