  Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum
state is impossible. But since imperfect cloning is still possible, a question
arises: "Is there an optimal quantum cloning machine?" Buzek and Hillery answer
to this question and construct their famous B-H quantum cloning machine. The
B-H machine clones state of an arbitrary single qubit in optimal manner and
hence it is universal. Generalizing this machine for two-qubit system is
straightforward, but this procedure does not preserve quantum correlation
existing in bipartite state in optimal manner and also, during this procedure,
this machine loses its universality and becomes a state-dependent cloning
machine. In this paper we propose an optimal universal local quantum state
cloner for two qubit systems. Also we present two classes of state-dependent
local quantum copying machine. Furthermore, we investigate local broadcasting
of two aspects of quantum correlations, i.e., quantum entanglement and quantum
discord defined, respectively, within the entanglement-separability paradigm
and from an information-theoretic perspective. The results show that although
quantum correlation is in general very fragile during broadcasting procedure,
quantum discord is broadcasted more robustly than quantum entanglement.
