  We consider the remote state restoring and perfect transfer of the zero-order
coherence matrix (PTZ) in a spin system governed by the XXZ-Hamiltonian
conserving the excitation number. The restoring tool is represented by several
nonzero Larmor frequencies in the Hamiltonian. To simplify the analysis we use
two approximating models including either step-wise or pulse-type
time-dependence of the Larmor frequencies. Restoring in spin chains with up to
20 nodes is studied. Studying PTZ, we consider the zigzag and rectangular
configurations and optimize the transfer of the 0-order coherence matrix using
geometrical parameters of the communication line as well as the special unitary
transformation of the extended receiver. Overall observation is that XXZ-chains
require longer time for state transfer than XX-chains, which is confirmed by
the analytical study of the evolution under the nearest-neighbor approximation.
We demonstrate the exponential increase of the state-transfer time with the
spin chain length.
