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Explore a captivating journey through quantum information theory in this 45-minute talk by Dr. Martin Plavala from Universität Siegen. Delve into the foundational problem of entanglement existence in non-classical operational theories, tracing its roots to George Barker's work in the 1970s. Discover the proof that entanglement is a generic feature of non-classical theories and learn about the development of mathematical tools for detecting entanglement across operational theories. Examine the generalization of the Doherty-Parrilo-Spedalieri (DPS) hierarchy and its applications in finite cases. Uncover unexpected applications of these findings in solving current quantum information problems, with a focus on the semi-device independent certification of Schmidt number in quantum states. Gain insights into the derivation of a tight SDP hierarchy for this problem, bridging foundational concepts with practical applications in quantum computing and information theory.
