# Experimental and theoretical investigations of quantum state transfer and decoherence processes in quasi-one-dimensional systems in multiple-quantum NMR experiments

## TL;DR

This paper combines experimental and theoretical approaches to study quantum state transfer and decoherence in quasi-one-dimensional spin systems using multiple quantum NMR, revealing insights into quantum information processing.

## Contribution

It establishes a connection between MQ NMR dynamics and one-dimensional spin chain models, and develops a theory of decoherence that matches experimental results.

## Key findings

- Quantum state transfer can be organized along a linear chain.
- Theoretical predictions agree well with experimental data.
- Decoherence modeled by dipolar relaxation in 1D systems.

## Abstract

Multiple quantum (MQ) NMR methods \cite{Baum} are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian \cite{Baum} describing MQ NMR dynamics is related to the flip-flop Hamiltonian of a one-dimensional spin system in the approximation of the nearest neighbor interactions. As a result, it is possible to organize quantum state transfer along a linear chain. MQ NMR experiments are performed on quasi-one-dimensional chains of \BPChem{\^{19}F} nuclei in calcium fluorapatite \BPChem{Ca\_5(PO\_4)\_3F}. Relaxation of the MQ NMR coherences is considered as the simplest model of decoherence processes. A theory of the dipolar relaxation of the MQ NMR coherences in one-dimensional systems is developed. A good agreement of the theoretical predictions and the experimental data is obtained.