Morphisms of Quantum Confusability Graphs
Jennifer Zhu
It would be unrealistic to have an information channel — quantum or classical — that always sends information with absolute accuracy; that is, we must expect a channel to have noise. In 1956, Shannon introduced the notion of zero-error capacity of a noisy (classical) channel using the confusability graph of this channel. In 2010, Duan, Severini, and Winter developed the analogous notion (quantum confusability graphs) for quantum channels and show that one can recover various types of zero-error capacities of quantum channels. In the first half of this talk, we will see how these quantum confusability graphs are derived and how they subsume Shannon's notion of classical confusability graphs.
In the latter half of this talk, we will dip our toes into category theory. In the intervening years, quantum confusability graphs have found connections outside of quantum information theory to operator algebras and categorical quantum theory (and more!). Category theory seeks to understand mathematics by artfully abstracting away details. We will see an example-driven introduction to categories (e.g., the words "object," "morphism," "Set", "Vect," will make an appearance, but not "functor" nor "natural transformation). I may take a minute or two to explain why this is not just pointless mathematical generalization but rather mathematical poetry. We will then abstractly present quantum confusability graphs and their morphisms. Time permitting, we may explore the notion of categorical limits in general and in particular.
Location
QNC 1201
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