Entanglement and control operations in Ising interactions of bipartite qubits

TL;DR

This paper provides a detailed analysis of entanglement in a three-dimensional Ising model with inhomogeneous magnetic fields, exploring its relation to energy and spin, and proposes basic quantum control schemes for information transfer.

Contribution

It offers the first detailed solution of 3D Ising model evolution with inhomogeneous fields and develops entanglement witnesses and control methods for bipartite qubits.

Findings

Entanglement relates to energy and spin in the model.

Control schemes can preserve entanglement and transfer information.

Inhomogeneous magnetic fields influence entanglement properties.

Abstract

Entanglement generated by Ising model has been studied for several authors in order to understand the relation between it and magnetic properties of materials, principally using one or two dimensional models for two or more particles. In this work, Ising model evolution is solved in three dimensions for two parts including an inhomogeneous magnetic field, giving an detailed study of the entanglement properties derived from interaction. Some relations between entanglement and energy or spin are developed specifically to stablish candidates for entanglement witness. Finally, some basic quantum control operations are prescripted for this model as to preserve the properties of the system as for transfer information between the two parts. These last schemes of control are useful when initial state is completely known, to gain domain on the system. It prevents to introduce more sophisticated control schemes which normally are necessary when initial state is at least partially unknown.