Perfect Transfer of Many-Particle Quantum State via High-Dimensional Systems with Spectrum-Matched Symmetry

The quantum state transmission through the medium of high-dimensional many-particle system (boson or spinless fermion) is generally studied with a symmetry analysis. We discover that, if the spectrum of a Hamiltonianmatches the symmetry of a fermion or boson system in a certain fashion, aperfect quantum state transfer can be implemented without any operation onthe medium with pre-engineered nearest neighbor (NN). We also study a simplebut realistic near half-filled tight-binding fermion system with uniform NNhopping integral. We show that an arbitrary many-particle state near thefermi surface can be perfectly transferred to its translational counterpart.