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

Entanglement is considered as a basic physical resource for modern quantum applications in Quantum Information and Quantum Computation theories. Interactions able to generate and sustain entanglement are subject to deep research in order to have understanding and control on it, based on specific physical systems. Atoms, ions or quantum dots are considered a key piece in quantum applications because is a basic piece of developments towards a scalable spin-based quantum computer through universal and basic quantum operations. Ising model is a type of interaction which generates and modifies entanglement properties of quantum systems based on matter. In this work, a general anisotropic three dimensional Ising model including an inhomogeneous magnetic field is analyzed to obtain their evolution and then, their algebraic properties which are controlled through a set of physical parameters. Evolution denote remarkable group properties when is analyzed in a non local basis, in particular those related with entanglement. These properties give a fruitful arena for further quantum applications and their control.