C. W. J. Beenakker, A. Grabsch, Y. Herasymenko
SciPost Phys. 6, 022 (2019) ·
published 11 February 2019

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Majorana zeromodes bound to vortices in a topological superconductor have a
nonAbelian exchange statistics expressed by a nondeterministic fusion rule:
When two vortices merge they may or they may not produce an unpaired fermion
with equal probability. Building on a recent proposal to inject edge vortices
in a chiral mode by means of a Josephson junction, we show how the fusion rule
manifests itself in an electrical measurement. A $2\pi$ phase shift at a pair
of Josephson junctions creates a topological qubit in a state of eveneven
fermion parity, which is transformed by the chiral motion of the edge vortices
into an equalweight superposition of eveneven and oddodd fermion parity.
Fusion of the edge vortices at a second pair of Josephson junctions results in
a correlated charge transfer of zero or one electron per cycle, such that the
current at each junction exhibits shot noise, but the difference of the
currents is nearly noiseless.