# Electron-Tunneling-Assisted Non-Abelian Braiding of Rotating Majorana Bound States

## TL;DR

This paper proposes a novel method to demonstrate non-Abelian statistics of Majorana bound states by using electron tunneling to actively manipulate fermion parity during their rotation, revealing new interference effects.

## Contribution

It introduces a theory where tunneling-induced parity changes enable non-Abelian braiding detection, challenging the view that parity fluctuations are purely harmful.

## Key findings

- Resonant tunneling current reveals interference from non-commuting braiding operations.
- Tunneling events change fermion parity, enabling active control of non-Abelian states.
- The approach demonstrates a new way to utilize parity fluctuations for quantum information processing.

## Abstract

It has been argued that fluctuations of fermion parity are harmful for the demonstration of non-Abelian anyonic statistics. Here, we demonstrate a striking exception in which such fluctuations are actively used. We present a theory of coherent electron transport from a tunneling tip into a Corbino geometry Josephson junction where four Majorana bound states (MBSs) rotate. While the MBSs rotate, electron tunneling happens from the tip to one of the MBSs thereby changing the fermion parity of the MBSs. The tunneling events in combination with the rotation allow us to identify a novel braiding operator that does not commute with the braiding cycles in the absence of tunneling, revealing the non-Abelian nature of MBSs. The time-averaged tunneling current exhibits resonances as a function of the tip voltage with a period that is a direct consequence of the interference between the non-commuting braiding operations. Our work opens up a possibility for utilizing parity non-conserving processes to control non-Abelian states.