Quantum Entanglement involved in Grover's and Shor's algorithms: the four-qubit case

In this paper, we study the nature of entanglement in quantum Grover's and Shor's algorithms. So far, the authors who have been interested in this problem have approached the question quantitatively by introducing entanglement measures (numerical ones most of the time). One can ask a different question: what about a qualitative measure of entanglement ? In other words, we try to find what are the different entanglement SLOCC classes that can be generated by these two algorithms. We treat in this article the case of pure four-qubit systems.Comment: 33 pages, 10 figures, 2 algorithm