  In classical information theory one can, in principle, produce a perfect copy
of any input state. In quantum information theory, the no cloning theorem
prohibits exact copying of nonorthogonal states. Moreover, if we wish to copy
multiparticle entangled states and can perform only local operations and
classical communication (LOCC), then further restrictions apply. We investigate
the problem of copying orthogonal, entangled quantum states with an entangled
blank state under the restriction to LOCC. Throughout, the subsystems have
finite dimension D. We show that if all of the states to be copied are
non-maximally entangled, then novel LOCC copying procedures based on
entanglement catalysis are possible. We then study in detail the LOCC copying
problem where both the blank state and at least one of the states to be copied
are maximally entangled. For this to be possible, we find that all the states
to be copied must be maximally entangled. We obtain a necessary and sufficient
condition for LOCC copying under these conditions. For two orthogonal,
maximally entangled states, we provide the general solution to this condition.
We use it to show that for D=2,3, any pair of orthogonal, maximally entangled
states can be locally copied using a maximally entangled blank state. However,
we also show that for any D which is not prime, one can construct pairs of such
states for which this is impossible.
