M-neighbor approximation in one-qubit state transfer along zigzag and alternating spin-1/2 chains

We consider the $M$-neighbor approximation in the problem of one-qubit pure state transfer along the $N$-node zigzag and alternating spin chains governed by the $XXZ$-Hamiltonian with the dipole-dipole interaction. We show that always $M>1$, i.e., the nearest neighbor approximation is not applicable to such interaction. Moreover, only all-node interaction ($M=N-1$) properly describes the dynamics in the alternating chain. We reveal the region in the parameter space characterizing the chain geometry and orientation which provide the high-probability state-transfer. The optimal state-transfer probability and appropriate time instant for the zigzag and alternating chains are compared.