  We investigate the exploitation of various combinatorial properties of graphs
and set systems to study several issues in quantum information theory. We
characterize the combinatorics of distributed EPR pairs for preparing
multi-partite entanglement in a real communication network. This combinatorics
helps in the study of various problems in multi-party case by just reducing to
the two-party case. Particularly, we use this combinatorics to (1) study
various possible and impossible transformations of multi-partite states under
LOCC, thus presenting an entirely new approach, not based on entropic
criterion, to study such state transformations. (2) present a protocol and
proof of its unconditional security for quantum key distribution amongst
several trusted parties. (3) propose an idea to combine the features of quantum
key distribution and quantum secret sharing. We investigate all the above
issues in great detail and finally conclude briefly with some open research
directions based on our research.
