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

Abstract

Abstract 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.