Ivan Todorov (QUB)

will speak on

Capacity bounds for non-commutative graphs

Time: 3:00PM
Date: Tue 12th November 2019
Location: Seminar Room SCN 1.25 [map]

Abstract: Non-commutative graphs - or, equivalently, operator subsystems of matrix algebras - arise naturally in quantum information theory as confusability graphs of quantum channels and play an important role in questions about zero-error information transmission. As in the classical case, the computation of the Shannon capacity of a non-commutative graph is a difficult problem that leads to the need to introduce easier computable bounds. In this talk, I will summarise some recent developments in this direction. In particular, I will describe non-commutative versions of the vertex packing polytope, the theta convex body and the fractional vertex packing polytope of a graph, and discuss a quantum version of the Sandwich Theorem of Grotschel, Lovasz and Schrijver. This leads to new non-commutative versions of the Lovasz number of a graph and an upper bound of the zero-error capacity of the corresponding quantum channel that can be genuinely better than the one originally established by Duan, Severini and Winter. I will also discuss non-commutative counterparts of several other widely used classical graph parameters and their interrelation.


This is joint work with Gareth Boreland and Andreas Winter.

(This talk is part of the Analysis series.)

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