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Analysis Seminar: An operator system approach to quantum correlations

Event Type
341 Altgeld
Mar 24, 2022   2:00 pm  
Travis Russell
Roy Araiza

In this talk, I will explain a novel approach to Tsirelson's problem using the theory of operator systems. Tsirelson's problem relates to whether the commuting operator model of quantum mechanics produces different statistics than the tensor product model of quantum mechanics in non-local measurement scenarios. These questions have been shown to be equivalent to Connes' embedding problem from the theory of Von Neumann algebras. After tremendous effort by physicists, mathematicians, and computer scientists, Tsirelson's problem was finally resolved in a recent paper. Nevertheless, interest in understanding Tsirelson's problem in greater detail remains. After exploring some background in the theory of operator systems, I will explain how to characterize quantum correlations using only abstract operator system theory, building upon existing C*-algebraic and operator theoretic characterizations in the literature. This new characterization yields an equivalent restatement of Tsirelson's problem in the language of abstract operator systems.

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