Quantum Information Theory

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This research project is concerned with mathematical problems that arise in the description of noisy quantum systems. Some of the work addresses the question of when entanglement can enhance the capacity of a noisy quantum channel. This includes work on longstanding conjectures and related questions about operator spaces. The project also investigates aspects of quantum error correction beyond the familiar stabilizer codes. Finally, the work addresses several mathematical questions that arise in adiabatic quantum computation and may shed light on the controversial issue of whether or not adiabatic quantum optimization can solve hard problems in polynomial time.brbrPhysicists have made considerable progress in demonstrating that quantum systems can be used for new methods of cryptography, communication, and computation. Further development of efficient, practical quantum communication systems requires theoretical investigations analogous to the fundamental work in classical communication theory on channel capacity and error correction. This project investigates several such mathematical issues directly connected to the practical implementation of quantum information processing.