College of Liberal Arts & Sciences

# Operator Theory Seminar

**Abstract:**

Various sets of correlations that arise in quantum information theory are in fact determined by tuples of commuting projections (with some other natural properties) on some Hilbert space. Thus, in a similar spirit to that of algebras of bounded operators, we have that these ``projection-valued measures'' serve as building blocks of correlation sets of particular interest. In recent years questions arising in quantum information theory have made their way into the minds of operator algebraists. In recent work with Travis Russell (West Point) we have developed the notion of a projection in an operator system and have used this to give a purely abstract characterization of so-called quantum commuting correlations. I will present how one can detect such a projection and how we used this to study correlation sets of particular interest. As time allows I will discuss joint/ongoing work with Travis Russell and Mark Tomforde

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