  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 $1 \to 2$ and the more general $1 \to N$ 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.
