Title. Quantum correlations, factorizable channels, and the Connes Embedding Problem
Abstract. The study of quantum correlations arising under two different assumptions of commutativity of observables, initiated by Tsirelson in the 80’s, has proven over the last decade to have deep interconnections with important problems in operator algebras theory, including various reformulations of the Connes Embedding Problem. In very recent work with M. Rørdam, we show that in every dimension n ≥ 11, the set of n×n matrices of correlations arising from unitaries in finite dimensional von Neumann algebras is not closed. As a consequence, in each such dimension there are quantum channels that admit type II1-von Neumann algebras as ancillas, but not finite dimensional ones, thus witnessing new infinite dimensional phenomena in quantum information theory. I will further discuss a reformulation (obtained in joint work with U. Haagerup) of the Connes embedding problem in terms of an asymptotic property of quantum channels possessing a certain factorizability property that originates in operator algebras, and a new viewpoint on factorizable channels, recently developed together with M. Rørdam, that gives rise to a new link.
LOCATION:Jefferson 356 STATUS:CONFIRMED DTSTART:20190402T200000Z DTEND:20190402T200000Z END:VEVENT END:VCALENDAR