Some Aspects of Remote State Restoring in State Transfer Governed by XXZ-Hamiltonian

TL;DR

This paper investigates remote state restoring and perfect transfer in XXZ spin chains, analyzing the effects of Larmor frequencies and chain configurations, and finds transfer times grow exponentially with chain length.

Contribution

It introduces models with step-wise and pulse-type Larmor frequency variations to optimize state transfer in XXZ spin chains, extending understanding of transfer dynamics.

Findings

XXZ chains require longer transfer times than XX chains.

Transfer time increases exponentially with chain length.

Optimization of transfer involves geometrical parameters and unitary transformations.

Abstract

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.