CQIS: RUI: Quantum State Symmetry and Applications

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Recent cutting-edge and near-future quantum devices will push the boundaries of information processing in communication, computation, and measurement in ways that will probe new physical realms and enhance the foundational understanding of physics. This project studies quantum entanglement and other nonlocal properties that power the "quantum advantage" of these revolutionary technologies. The PI seeks to design useful applications for quantum computers and quantum communication networks. In addition to achieving scientific progress through new results, a major project component is scientific development of undergraduate students through participation in real research.This project will implement a systematic framework studying local unitary and permutational symmetries of many-body states to probe multiparticle quantum entanglement and to develop applications for quantum protocols. A main tool for entanglement analysis is the use of isotropy subgroups (that is, the set of unitaries that leave a given state invariant) of the group of local operations; the isomorphism classes of these isotropy groups are entanglement invariants that can be used not only for classification, but also for designing algorithms and protocols. Methodology includes the theory of Lie groups and Lie algebras, representation theory and Schur-Weyl duality, together with the proposer's past results.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.