  A single quantum state can be shared by many distant parties. In this thesis,
we try to characterize the information contents of such distributed states by
defining the multiparty information and the multiparty squashed entanglement,
two steps toward a general theory of multiparty quantum information. As a
further step in that direction, we partially solve the multiparty distributed
compression problem where multiple parties use quantum communication to
faithfully transfer their shares of a state to a common receiver. We build a
protocol for multiparty distributed compression based on the fully quantum
Slepian-Wolf protocol and prove both inner and outer bounds on the achievable
rate region. We relate our findings to previous results in information theory
and discuss some possible applications.
