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In this paper, we study the nature of entanglement in quantum Grover's andShor's algorithms. So far, the authors who have been interested in this problemhave approached the question quantitatively by introducing entanglementmeasures (numerical ones most of the time). One can ask a different question:what about a qualitative measure of entanglement ? In other words, we try tofind what are the different entanglement SLOCC classes that can be generated bythese two algorithms. We treat in this article the case of pure four-qubitsystems.

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