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

### Submission summary

 As Contributors: Carlo Beenakker · Aurélien Grabsch · Yaroslav Herasymenko Arxiv Link: https://arxiv.org/abs/1812.01444v1 Date submitted: 2018-12-05 Submitted by: Beenakker, Carlo Submitted to: SciPost Physics Domain(s): Theoretical Subject area: Quantum Physics

### Abstract

Majorana zero-modes bound to vortices in a topological superconductor have a non-Abelian exchange statistics expressed by a non-deterministic 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 even-even fermion parity, which is transformed by the chiral motion of the edge vortices into 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 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.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1812.01444v1 (5 December 2018)