This thesis investigates quantum cloning and related quantum entanglement problems using core concepts of representation theory, in particular those associated with the symmetric group. The research explores Schur-Weyl duality and its extensions, which allow efficient representation and manipulation of quantum systems, serving as a valuable tool for quantum information theory. A primary application of Schur-Weyl duality is the quantum cloning problem, which is studied for both the
1→2 and the more general
1→N cases, providing new insights into the constraints imposed by the no-cloning theorem. The investigation extends to a more general quantum entanglement problem on a complete graph.