The logic and topology of non-locality and contextuality

Abstract

Bell's theorem famously shows that no local theory can account for the predictions of quantum mechanics; while the Kochen-Specker theorem shows the same for non-contextual theories. Non-locality, and increasingly also contextuality, play an important role as computational resources in current work on quantum information. Much has been written on these matters, but there is surprisingly little unanimity even on basic definitions or the inter-relationships among the various concepts and results. We use the mathematical language of sheaves and monads to give a very general and mathematically robust description of the behaviour of systems in which one or more measurements can be selected, and one or more outcomes observed. In particular, we give a unified account of contextuality and non-locality in this setting. © 2011 Springer-Verlag Berlin Heidelberg.