Title: Non-commutative disintegration Speaker: Arthur Parzygnat (University of Connecticut)
Time: Friday, October 26, 2018 at 3:30 pm Place: MONT 414Abstract: The notion of a disintegration of positive measures can be formulated diagrammatically in a category of measure spaces and transition kernels. Combining this with the functor relating transition kernels to positive operators on C*-algebras, a notion of non-commutative disintegration can be made for states on C*-algebras. While a certain degree of uniqueness holds as in the classical measure-theoretic case, existence of such disintegrations is not guaranteed even on finite-dimensional matrix algebras. Such disintegrations are closely related to reversible quantum channels in quantum information theory and non-commutative conditional probabilities. This is joint work with Benjamin P. Russo (Farmingdale State College SUNY).