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.
The major goals of the project are to advance our understanding on the power and limitations of quantum information processing (QIP), in particular with respect to the roles of entanglement and its manipulations, to educate the new generations of researchers in QIP, and to engage the faculty and students at University of Michigan on QIP research. To that end, multiple research projects on a wide range of problems were investigated intensively. The participants include researchers at many levels, from faculty members, postdocs, PhD students, to undergraduate students. A weekly reading seminar has attracted participations from several departments and at several levels. Together with other sources of funding, the award supported a professor (the PI),a postdoctoral scholar, a PhD student, and two undergraduate students. The award supportedin part 1 PhD thesis, 9 papers in journals or peer-reviewed conferences and 2 manuscripts awaiting publications. Highlights of the research findings include characterizations of the communication costfor creating quantum states in a distributed setting and for solving some distributed problems,characterizations of the advantage of quantum entanglement in assisting communicationsover noisy classical channels, characterizations of the robust self-testing properties of untrustedquantum devices, and methods for securely and robustly generating randomness and distributingsecret keys using untrusted quantum devices.
