Perfect information transfer in neighbor-coupled spin chains

We study how to engineer parameters for perfect information transfer in neighbor-coupled spin chains. The 2^N-dimensional Hilbert space associated with quantum information transfer over the spin chain can be projected into an N-dimensional subspace, so the Hamiltonian of the system will be reduced to a tridiagonal matrix in a standard basis. The functional relation between the parameters of the spin chain and the eigenvalue spectrum of the Hamiltonian, which can be determined by the perfect transfer conditions, are established. The task of finding all solutions to the parameters of perfect information transfer is accomplished by solving polynomial equations. All analytical solutions from 3 qubits to 9 qubits are presented. The results could be used to analyze structures of the chain or find particular chains with optimal properties.