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Entanglement is considered as a basic physical resource for modern quantumapplications in Quantum Information and Quantum Computation theories.Interactions able to generate and sustain entanglement are subject to deepresearch in order to have understanding and control on it, based on specificphysical systems. Atoms, ions or quantum dots are considered a key piece inquantum applications because is a basic piece of developments towards ascalable spin-based quantum computer through universal and basic quantumoperations. Ising model is a type of interaction which generates and modifiesentanglement properties of quantum systems based on matter. In this work, ageneral anisotropic three dimensional Ising model including an inhomogeneousmagnetic field is analyzed to obtain their evolution and then, their algebraicproperties which are controlled through a set of physical parameters. Evolutiondenote remarkable group properties when is analyzed in a non local basis, inparticular those related with entanglement. These properties give a fruitfularena for further quantum applications and their control.

Algebraic and group structure for bipartite three dimensional anisotropic Ising model on a non-local basis