Thursday, August 4, 2022 — 10:00 AM EDT

Nicholas Manor,  Department of Pure Mathematics, University of Waterloo

"Quantum Channels, Exactness, and Noncommutative Convexity"

This presentation will consist of three short sections discussing separate topics of my PhD research.

Section one will discuss joint work with Matthew Kennedy and Vern Paulsen about the connection between PPT (positive partial transpose) quantum channels and their connection to entanglement. We show that when a PPT channel is composed with itself repeatedly, the composition becomes entanglement breaking in the limit.

Section two will discuss exactness for locally compact groups and the exactness of the associated reduced C*-algebra. We show that for a broad class of well behaved groups these two properties coincide.

Section three is the largest and will discuss two projects on nc (noncommutative) convexity: the first is joint work with Matthew Kennedy and Se-Jin Kim, and the second is joint work with Adam Humeniuk and Matthew Kennedy. Davidson-Kennedy showed that there is a natural duality between operator systems and compact nc convex sets, and we extend this result to nonunital operator systems, i.e., norm closed self-adjoint subspaces of B(H).

More recently, C.K. Ng studied the duals of nonunital operator systems and asked whether these duals are again operator systems. They answered this question by algebraically characterizing operator systems with operator system duals. We expand on this work by providing a characterization in terms of the geometric structure of the compact nc convex set of completely contractive and completely positive maps on an operator system.

Online. Contact Nick Manor (nmanor@uwaterloo.ca) for more information.

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