  In the first part of this Dissertation, I study the differences between LOCC
(local operations and classical communication) and the more general class of
separable operations. I show that the two classes coincide for the case of pure
bipartite state input, and derive a set of important consequences. Using
similar techniques I also generalize the no-cloning theorem when restricted to
separable operations and show that cloning becomes much more restrictive, by
providing necessary (and sometimes sufficient) conditions.
  In the second part I investigate graph states and graph codes with carrier
qudits of arbitrary dimensionality, and extend the notion of stabilizer to any
dimension, not necessarily prime. I further study how and where information is
located in the various subsets of the qudit carriers of arbitrary additive
graph codes, and provide efficient techniques that can be used in deciding what
types of information a subset contains.
