Local Adiabatic Mixing of Kramers Pairs of Majorana Bound States

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.

5 pages. Misprints in Eqs. (7) and (8a) corrected

References in corpus (3)

• Non-Abelian Anyons and Topological Quantum Computation
• Introduction to topological superconductivity and Majorana fermions
• Majorana bound states and non-local spin correlations in a quantum wire on an unconventional superconductor

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