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Majorana zero-modes bound to vortices in a topological superconductor have anon-Abelian exchange statistics expressed by a non-deterministic fusion rule:When two vortices merge they may or they may not produce an unpaired fermionwith equal probability. Building on a recent proposal to inject edge vorticesin a chiral mode by means of a Josephson junction, we show how the fusion rulemanifests itself in an electrical measurement. A $2\pi$ phase shift at a pairof Josephson junctions creates a topological qubit in a state of even-evenfermion parity, which is transformed by the chiral motion of the edge vorticesinto an equal-weight superposition of even-even and odd-odd fermion parity.Fusion of the edge vortices at a second pair of Josephson junctions results ina correlated charge transfer of zero or one electron per cycle, such that thecurrent at each junction exhibits shot noise, but the difference of thecurrents is nearly noiseless.

Electrical detection of the Majorana fusion rule for chiral edge vortices in a topological superconductor