University of Oxford, UK, amy.searle@physics.ox.ac.uk
(joint work with Samson Abramsky and Rui Soares Barbosa)
Following on from the work presented by Samson Abramsky, we describe how the framework developed therein can be used to classify the non-classicality of new examples in the literature as contextual. In doing so, we gain a deeper understanding of the assumptions of classicality which are implicitly made. In particular, we classify two types of event enablings (in the language of Plotkin-Nielsen-Winskel) which could be present: at the system level and at the level of the verifier or experimenter— together these enablings describe how measurements may unfold in time. In doing so, the contextual setups and the definite causal setups of Abramsky-Brandenburger and Gogioso-Pinzani, respectively, as well as examples in which outcomes of measurements are fed forward to determine the choice of future measurements, can be understood as special cases of this general framework. The measurement scenarios of contextual setups and definite causal setups are in fact those generated by repeated application of series and parallel composition operators to simple ‘building block’ measurement scenarios. We see that classicality, arising as a global section of the relevant presheaf, depends crucially on (i) whether measurements have total or partial access to those measurement which occurred in their history and (ii) to which combinations of measurements the experimenter has access, as might be enforced by feedforward of measurement outcomes.