  The intriguing and powerful capability of nonlocality in communication field
ignites the research of the nonlocality distillation. The first protocol
presented in Ref[Phys. Rev. Lett. 102, 120401] shows that the nonlocality of
bipartite binary-input and binary-output nonsignaling correlated boxes could be
amplified by 'wiring' two copies of weaker-nonlocality boxes. Several optimized
distillation protocols were presented later for bipartite binary-input and
binary-output nonsignaling correlated boxes. In this paper, we focus on the
bipartite binary-input and multi-nary-output nonsignaling correlated
boxes---high-dimensional boxes, and design comparators-based protocols to
achieve the distillation of high-dimensional nonlocality. The results show that
the high-dimensional nonlocality can be distilled in different ways, and we
find that the efficiencies of the protocols are influenced not only by the
wirings but also by the classes the initial nonlocality boxes belongs to. Here,
the initial nonlcalities may have the same violation of the high-dimensional
Bell-type inequality, but they can fall into different classes, which shows
that the value of the violation of the high-dimensional Bell-type inequality is
not the only representation of nonlocality, and the combination manner(classes)
in the expression of the correlated boxes is another important nonlocal
representation too. The current protocols are compatible with the previous
two-dimensional nonlocality distillation protocols, but our protocols are more
powerful and universal than previous ones in the sense that the current
protocols can be applied to the system with any dimension rather than the only
two-dimension system in the previous protocols.
