An operator system approach to quantum correlations


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.


Our C*-Seminar will still (as it was last year) be on Wednesdays, but the time will now be a bit different: 1:30-2:45 pm (Arizona time, no daylight savings), meeting both in person (WXLR A309) and via zoom.

Also new: it's now the ASUERAU C*-Seminar (so, joint with our friends Lara and Mitch at Embry-Riddle Aeronautical University up the road in Prescott).

(Please email the organizer John Quigg to be put on the email list if you would like to receive the link to the zoom seminar.)


Travis Russell
Assistant Professor
Army Cyber Institute
United States Military Academy, West Point, NY

WXLR A309 and virtual via Zoom