  The spin-dependent scattering process in a system of topological insulator
and quantum dot is studied. The unitary scattering process is viewed as a gate
transformation applied to an initial state of two electrons. Due to the
randomness imposed through the impurities and alloying-induced effects of band
parameters, the formalism of the random unitary gates is implemented. For
quantifying entanglement in the system, we explored concurrence and
ensemble-averaged R\'enyi entropy. We found that applied external magnetic
field leads to long-range entanglement on the distances much larger than the
confinement length. We showed that topological features of itinerant electrons
sustain the formation of robust long-distance entanglement, which survives even
in the presence of a strong disorder.
