M. Plavala: Foundational problems, mathematical results and applications in quantum information
Channel: Centrum Fizyki Teoretycznej PAN
Date: 11/05/2023

Dr Martin Plavala (Universität Siegen).
A tale of unexpected consequences: From foundational problems to mathematical results and applications in quantum information.
This talk begins with the problem of whether entanglement exists in all non-classical operational theories. This problem was already considered as a mathematical problem by George Barker in the 70' in the context of ordered vector spaces; here we discuss some aspects of the proof that entanglement is a generic feature of non-classical theories. As a consequence of this result, the need for mathematical tools to detect entanglement in all operational theories arises, we address this issue by presenting a generalization of the Doherty-Parrilo-Spedalieri (DPS) hierarchy to operational theories, and we also mention the cases when such a hierarchy is finite. Finally, we discuss the unexpected applications of these results to solve current problems in quantum information, we mainly focus on the problem of semi-device independent certification of Schmidt number of quantum states, for which we derive a tight SDP hierarchy.
Quantum Information and Quantum Computing Seminars CTP PAS
2023-05-04