AF: CIF: Small: Theoretical Studies in Quantum Information and Computation

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This project aims to deepen our understanding on two fundamental aspects of quantum information processing.(1) Entanglement manipulations and classifications. Quantum entanglement plays a central role in quantum information processing. An objective of the theory of quantum entanglement is to classify different types of entanglement according to their inter-convertibility through manipulations that do not require quantum communication. While bipartite entanglement is well understood in this framework, entanglement among three or more subsystems is inherently much more difficult. The PI is investigating properties of multipartite, especially tripartite, entanglement, with an emphasis of the algorithmic/computational complexity perspective. (2) Communication complexity. Communication complexity studies the inherent communication cost for distributed computing. This project addresses three important and related open problems: the Log-Rank Conjecture for characterizing the deterministic complexity; finding the largest possible gaps between the quantum and classical complexities; and the question if entanglement can dramatically reduce the cost for quantum communication. The plan to attack those difficult problems is to focus on some restricted classes of functions that are simple yet on which the problems remain open and challenging.