  The quantum state transmission (QST) through the medium of high-dimensional
many-particle system is studied with a symmetry analysis. We discover that, if
the spectrum matches the symmetry of a fermion or boson system in a certain
fashion, a perfect quantum state transfer can be implemented without any
operation on the medium. Based on this observation the well-established results
for the QST via quantum spin chains can be generalized to the high-dimensional
many-particle systems with pre-engineered nearest neighbor (NN) hopping
constants. By investigating a simple but realistic near half-filled
tight-binding fermion system with uniform NN hopping integral, we show that an
arbitrary many-particle state near the fermi surface can be perfectly
transferred to its translational counterpart.
