Proposal for reading out anyon qubits in non-abelian $\nu = 12/5$ quantum Hall state

TL;DR

This paper proposes a method to detect non-abelian anyon statistics in the $ u=12/5$ quantum Hall state using interferometry, highlighting differences from the $ u=5/2$ state and discussing superposition states.

Contribution

It extends interferometric detection techniques to the $ u=12/5$ state, analyzing how internal quasihole states affect interference amplitudes.

Findings

Interference amplitude depends on quasihole internal states.

Amplitude is independent of the number of quasiholes in this state.

Additional interferometer features are needed for superposition states.

Abstract

To detect non-abelian statistics in the $\nu = 12/5$ quantum Hall state through interferometry, we apply an analysis similar to the ones proposed for the non-abelian $\nu = 5/2$ quantum Hall state. The result is that the amplitude of the Aharonov-Bohm oscillation of this interference is dependent on the internal states of quasiholes, but, in contrast to the $\nu = 5/2$ quantum Hall state, independent of the number of quasiholes. However, if the quasiholes are in a superposition state, it is necessary for the interferometer to have certain additional features to obtain the coefficients.