LFCS Seminar: 18 September 2019 - Samson Abramsky

Title: Simulations of quantum resources and the degrees of contextuality

Abstract:

(Joint work with Rui Soares Barbosa, Martti Karvonen, and Shane Mansfield)

 A key objective in the field of quantum information and computation is to understand the advantage which can be gained in information processing tasks by the use of quantum resources. While a range of examples have been studied, to date a systematic understanding of quantum advantage is lacking.

Our focus here is on quantum resources which take the form of \emph{non-local}, or more generally \emph{contextual}, correlations. Contextuality is one of the key signatures of non-classicality in quantum mechanics, and has been shown to be a necessary  ingredient for quantum advantage in a range of information processing tasks. We will describe a notion of simulation between quantum resources, and more generally between resources described in terms of contextual correlations, in the `sheaf-theoretic'  framework for contextuality (Abramsky-Brandenburger). The notion of simulation is expressed as a morphism of empirical models, in a form which allows the behaviour of one set of correlations to be simulated in terms of another using classical processing and shared randomization. Mathematically, this is expressed as coKleisli maps for a comonad of ``measurement protocols'' on the category of empirical models. 

The talk will be essentially self-contained, introducing the various notions we will discuss.