A hierarchy in Majorana non-abelian tests and hidden variable models

TL;DR

This paper develops classical hidden variable models to analyze the limitations of Majorana non-abelian tests, establishing a hierarchy of tests with increasing complexity to ensure loophole-free verification.

Contribution

It introduces a hierarchy of classical models that clarify the boundaries and limitations of Majorana non-abelian tests, aiding in designing more reliable experiments.

Findings

Identifies a hierarchy among Majorana tests based on experimental complexity.

Classical models can replicate certain properties of Majorana systems.

Highlights potential loopholes and the need for careful test design.

Abstract

The recent progress of the Majorana experiments paves a way for the future tests of non-abelian braiding statistics and topologically-protected quantum information processing. However, a deficient design in those tests could be very dangerous and reach false-positive conclusions. A careful theoretical analysis is necessary in order to develop loophole-free tests. We introduce a series of classical hidden variable models to capture certain key properties of Majorana system: non-locality, topologically non-triviality, and quantum interference. Those models could help us to classify the Majorana properties and to set up the boundaries and limitations of Majorana non-abelian tests: fusion tests, braiding tests and test set with joint measurements. We find a hierarchy among those Majorana tests with increasing experimental complexity.