Analytic next-to-nearest-neighbor $XX$ models with perfect state transfer and fractional revival

Certain nonuniformly coupled spin chains can exhibit perfect transfer of quantum states from end to end. Motivated by recent experimental implementations in evanescently coupled waveguide arrays, we extend the simplest such chain to next-to-nearest-neighbor couplings. It is shown analytically that perfect state transfer can be maintained under the extension and that end-to-end entanglement generation (fractional revival) can occur.