Analytic aspects of quantum information theory

The famous Einstein-Podolsky-Rosen paper from 1935 demonstrated, in a seemingly paradoxical way, how entanglement is an integral part of quantum mechanics, and the authors questioned if this consequence of quantum mechanics is real. This was later confirmed, first mathematically via Bell's inequalities, and subsequently by the Nobel prize winning experiment of Aspect in the early 1980s. Entanglement, which has no classical counterpart, is a central feature in quantum information theory (QIT). It has a beautiful, and at the same time elusive, mathematical description. In this project, that will be carried out at UCLA, we will study the mathematical theory behind entanglement, using techniques from analysis, to shed light on long-standing open problem in QIT.