  In this article we analyze the efficiency of operations based on transferring
charge from a quantum dot (QD) to two coupled topological superconductors,
which can be used for performing nonabelian operations on Majorana bound states
(MBSs). We develop a method which allows us to describe the full time-evolution
of the system as the QD energy is manipulated. Using a full counting statistics
analysis, we set bounds to the operation time scales. The lower bound depends
on the superconducting phase difference due to a partial decoupling of the
different MBSs parity sectors, while the upper bound is set by the tunneling of
quasiparticles to the MBSs. Using realistic parameters, we find the existence
of a regime where the operation can be carried out with a fidelity close to
unity. Finally, we propose the use of a two operations protocol to quantify the
effect of the dephasing and accumulated dynamical phases, demonstrating their
absence for certain superconducting phase differences.
