The No-Cloning Theorem describes the restrictions on the sets of pure states that can undergo the deterministic quantum cloning process, which is a quantum mechanical analogue of the classical copying process. Many generalizations of the deterministic quantum cloning process have been studied. These include probabilistic cloning, which aims to create perfect copies some of the time; approximate (a.k.a. universal) cloning, which aims to create less-than-perfect copies all of the time; and broadcasting, which generalizes the deterministic cloning process to account for mixed states.

In each of these processes, the composite quantum mechanical system is made up of two subsystems - one subsystem which starts in some state that we desire to copy, and the other subsystem which starts in some "blank" state, onto which we wish to make the copy. Furthermore, these two subsystems are assumed to be initially uncorrelated.

This talk will cover a description of two further generalizations of the deterministic quantum cloning process which allow the initial state of the compound system to be entangled. Such entangled initial states are necessary to consider if one wants to describe a quantum mechanical analogue of classical copying that is applicable to bosons. The restrictions on the sets of states that can undergo these generalized cloning processes will be discussed. A connection between these sets of states and the mathematical theory of graphs will be shown, along with a connection to probabilistic cloning.