All possible coupling schemes in XY spin chains for perfect state transfer

We investigate quantum state transfer in XY spin chains and propose a recursive procedure to construct the nonuniform couplings within these chains of arbitrary length in order to achieve perfect state transfer. We show that this method is capable of finding all possible coupling schemes for perfect state transfer. These schemes, without external control fields, involve analytically identified engineered couplings without the need for dynamical control. The analytical solutions provide all information for coupling design.