Local Adiabatic Mixing of Kramers Pairs of Majorana Bound States

TL;DR

This paper investigates how local adiabatic perturbations affect Kramers pairs of Majorana bound states, revealing potential vulnerabilities in their use as parity qubits due to induced rotations in their state space.

Contribution

It demonstrates that local adiabatic perturbations can cause rotations in Kramers pairs, providing analytical and numerical examples, and offers conditions to prevent such rotations.

Findings

Local adiabatic perturbations can rotate Kramers pairs.

Quantum information in Kramers pairs is not inherently protected.

Conditions to avoid rotations are identified and exemplified.

Abstract

We consider Kramers pairs of Majorana bound states under adiabatic time evolution. This is important for the prospects of using such bound states as parity qubits. We show that local adiabatic perturbations can cause a rotation in the space spanned by the Kramers pair. Hence the quantum information is unprotected against local perturbations, in contrast to the case of single localized Majorana bound states in systems with broken time reversal symmetry. We give an analytical and a numerical example for such a rotation, and specify sufficient conditions under which a rotation is avoided. We give a general scheme for determining when these conditions are satisfied, and exemplify it with a general model of a quasi 1D time reversal symmetric topological superconductor.