Quantum Resource Theories: General Structures and Fundamental Applications

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Quantum mechanics describes the subatomic world in ways that seem counterintuitive to our everyday experience. Recently, researchers have discovered innovative ways to harness these surprising features for use in information processing technologies. Quantum systems are now understood as possessing certain resources such as entanglement, coherence, and nonlocality, which can be applied in next-generation devices. This research project will study the general mathematical theory of quantum resources. It seeks to advance the understanding of how non-classical features of quantum mechanics can be measured and manipulated using physical processes that are conducive for experimental implementation. Ultimately the results of this project will help lay the theoretical foundation for future quantum-based technologies, which include cryptographic, computational, and communication devices. In attaining its results, this project will help prepare the next generation of scientists by supporting a diverse student workforce. This research will study quantum resource theories from two complementary perspectives. First, it will investigate general mathematical features that are present in many different types of quantum resource theories. Specifically, it will identify and study a general mathematical feature, known as full physical consistency, that naturally arises in resource theories strongly compatible with realistic experimental implementations. In addition, it will investigate structural properties and resource measures in non-convex theories. As a second research thrust, this project will examine the specific resource theories of quantum nonlocality and generalized quantum measurements. Rigorous frameworks for these resource theories will be developed that focus on their operational natures. Furthermore, nonlocality and measurement incompatibility, two fundamental features of quantum mechanics, will be unified as equivalent resources in semi-quantum nonlocal games. As a practical application, a novel method for constructing measurement device-independent dimensionality witnesses will be introduced.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.