  In the quantum system, perfect copying is impossible without prior knowledge.
But, perfect copying is possible, if it is known that unknown states to be
copied is contained by the set of orthogonal states, which is called the copied
set. However, if our operation is limited to local operations and classical
communications, this problem is not trivial. Recently, F. Anselmi, A. Chefles
and M.B. Plenio constructed theory of local copying when the copied set
consists of maximally entangled states. They also classified the copied set
when it consists of two orthogonal states (New. J. Phys. 6, 164 (2004)). In
this paper, we completely classify the copied set of local copying of the
maximally entangled states in the prime dimensional system. That is, we prove
that, in the prime dimensional system, the set of locally copiable maximally
entangled states is equivalent to the set of Simultaneously Schmidt
decomposable canonical form Bell states. As a result, we conclude that local
copying of maximally entangled states is much more difficult than local
discrimination at least in prime dimensional systems.
