Perfect transfer of many-particle quantum state via high-dimensional systems with spectrum-matched symmetry

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.