Quantum Information Theory and the Connes Embedding Problem (Magdalena Musat, University of Copenhagen)

23.03.2017 13:00

In 1980, Tsirelson showed that Bell’s inequalities that have played an important role in distinguishing classical correlations from quantum ones, and that were used to test, and ultimately disprove the Einstein-Podolski-Rosen postulate of “hidden variables", coincide with Grothendieck’s famous inequalities from functional analysis. Tsirelson further studied sets of quantum correlations arising under two different assumptions of commutativity of observables. While he showed that they are the same in the finite dimensional case, the equality of these sets was later proven to be equivalent to the most famous still open question in operator algebras theory: the Connes embedding problem. In recent joint work with Haagerup, we establish a different reformulation of the Connes embedding problem in terms of an asymptotic property of quantum channels posessing a certain factorizability property (that originates in operator algebras). Several concrete examples will be discussed.

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Room 17, Séminaire "Groupes et Géométrie"

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