CAREER: New Frontiers in Quantum Protocols, Operator Algebras, and Property Testing

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Over the past decade, the study of quantum multiprover interactive proofs (QMIPs) has deepened the understanding of the power of quantum entanglement as an information-processing resource. This research led to a recent quantum complexity result, known as MIP* = RE, which characterizes the computational power of QMIPs. Surprisingly, this characterization yields answers to longstanding problems in mathematical physics and operator algebras. Motivated by this, this project aims to explore the fascinating connections between complexity theory, quantum information, and pure mathematics. The overarching theme is to investigate how classical users can test and characterize complex quantum objects, with applications ranging from cryptography to operator algebras. These investigations will spur interdisciplinary research across computer science, physics, and mathematics. In addition to leading the research, the PI will disseminate this subject matter to a wide variety of communities (both academic and industrial). The PI will also participate in outreach and education activities, both in-person and online, to promote interest in quantum information science in high school and undergraduate students.This project will pursue three main directions. First, the PI will develop novel protocols that allow a classical user to verify complex quantum entanglement in untrusted quantum devices, with applications to entanglement theory and testing of noisy quantum computers. Second, the PI will further develop the techniques used in the proof of MIP* = RE to address unsolved questions in mathematics related to the resolutions of Tsirelson’s problem and Connes’ embedding problem. Third, the PI will initiate the systematic study of a noncommutative model of property testing, which will examine how local classical tests can constrain complex, quantum objects. This research will build upon prior work of the PI on interactive protocols for testing quantum entangled devices.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.