Charge-transfer based operations revealing non-abelian statistics of Majorana bound states

By now, there has been a lot of evidence of the existence of Majorana bound states (MBSs) at the ends of topological superconductors (TSs) [1]. However, a definitive proof of their topological origin will rely on the demonstration of their non-abelian statistics, emerging after the exchange of two or more MBSs in real space. Alternatively, MBSs can be exchanged in parameter space using charge-transfer operations using a quantum dot (QD) coupled to two TSs [2]. In this presentation I will analyze the efficiency of these operations [3]. Using a full counting statistics analysis, we set bounds to the optimal operation time scales. The lower bound depends on the phase difference, due to a partial decoupling of the different parity sectors. The upper bound is determined by poisoning processes due to the tunneling of quasiparticles to the MBSs. Using realistic parameters, we find that operations can be performed with a fidelity close to unity in the μs to ms timescales, demonstrating the absence of dephasing and accumulated dynamical phases.

[1] R. Lutchyn et al. Nat. Rev. Mat. 3, 52 (2019).
[2] K. Flensberg, Phys. Rev. Lett. 106, 090503 (2011).
[3] R. Seoane Souto, K. Flensberg and M. Leijnse. Phys. Rev. B 101, 081407 (2020)