  We propose a method to implement a kind of non-local operations between
spatially separated two systems with arbitrary high-dimensions by using only
low-dimensional qubit quantum channels and classical bit communications. The
result may be generalized straightforwardly to apply for multiple systems, each
of them with arbitrary dimensions. Compared with existed approaches, our method
can economize classical resources and the needed low-dimensional quantum
channels may be more easily established in practice. We also show the
construction of the non-local quantum XOR gate for qutrit systems in terms of
the obtained non-local operations as well as some single qutrit local gates.
