Problem statement Quantum information theory, the quantum extension of Shannon's classi- cal information theory, has experienced a surge of interest and rapid technical advance over the past ten years, largely in response to the development of quantum-mechanically based cryptographic protocols and algorithms for quantum computing. Very recent work by the Principal Investigator and collaborators has led to a grand unification" in the two-user setting, and much is now under- stood about the interplay between the plethora of quantum information processing resources such as quantum channels, entanglement and classical communication. As progress in the field has been hitherto guided by experiences from the classical theory, the next natural step is to investigate the quantum extensions of classical network (or multi-user) information theory. We propose a number of problems in quantum network information theory, including quantum versions of distributed compression, coding for multiple-access channels, broadcast channels and channels with state in- formation, and channel simulation with side information. Preliminary investigations indicate that many of the methods used in quantum two-user information theory apply to the multi-user setting, while revealing interesting new behaviour. Moreover, solutions to certain two-user problems may be interpreted in stunning new ways as solutions to long sought after multi-user ones. Intellectual merit This research will contribute to both quantum information theory and clas- sical network information theory. Multi-user scenarios shed new light on the properties of quantum information, in particular i) the ways in which two independent sources of quantum information may be used, despite their delicate nature, to decode each other; ii) the ways in which a distributed quantum source may be localized. On the other hand, quantizing" classical results has hitherto lead to several new techniques and re-interpretations of the classical theory. Broader impact This research will contribute to developing links between network information theory and quantum mechanics. On a more practical level, due to the traditional connection between quantumness and privacy, network quantum information theory bears relevance to multi- user quantum cryptography. There is perhaps only a handful of experts in quantum information theory currently in the US; the way to improve this it through education. The funding of this proposal would enable the training of PhD students in this area, and facilitate the introduction of this new material into the University of Southern California course curriculum. The Principal Investigator is developing a course on quantum information theory to be ordered in Fall 2005, covering topics not ordered at any other US university. He is also writing a book with co-authors A. Winter and P. Hayden entitled Principles of Quantum Information Theory".