Contextuality and quantum advantage
Abstract"The aim of the project is to explore the use of quantum resources to gain advantage over classical computational models in a range of tasks. The tasks which may be considered include: bounded-depth circuits, non-local games, measurement-based computation, communication complexity, and query complexity. High-level methods for describing quantum solutions for such problems will be studied, based on recent work on a structural theory of contextuality and its application to quantum advantage developed by Abramsky and co-workers. Both qualitative aspects - existence of perfect strategies or solutions - and quantitative aspects - contextuality monotones and resource inequalities - will be studied.
Contextual fraction as a measure of contextuality, Abramsky, Barbosa and Mansfield PRL 2017 The quantum monad, Abramsky, Barbosa, de Silva and Zapata, MFCS 2017. "