Irreducible noncontextuality inequalities from the Kochen-Specker theorem

Irreducible noncontextuality inequalities from the Kochen-Specker theorem

Seminar author:Ravi Kunjwal

Event date and time:05/31/2017 02:30:pm

Event location:GIQ seminar room C5/260

Event contact:

Recent work (Kunjwal and Spekkens, Phys. Rev. Lett. 115, 110403 (2015)) has shown how operational noncontextuality inequalities robust to noise can be obtained from Kochen-Specker uncolourable (or KS-uncolourable) hypergraphs without assuming that measurement outcomes are fixed deterministically by the ontic state of the system in an underlying ontological model. This result was obtained by an explicit numerical enumeration of all the extremal points of the polytope of (measurement) noncontextual assignments of probabilities to the KS-uncolourable hypergraph. I’ll focus on an analytical approach to deriving such noncontextuality inequalities that relies on constraints arising directly from the structure of the hypergraph without necessarily enumerating all the extremal probabilistic models on it. This cleanly identifies operational quantities that one can expect to be constrained (and why) by the assumption of noncontextuality instead of having to guess these quantities or obtaining them from brute-force numerical methods (such as Fourier-Motzkin elimination) without any guiding principles to identify them. This approach relies on giving such noncontextuality inequalities and their upper bounds an interpretation in terms of the hypergraph structure. I’ll demonstrate noncontextuality inequalities robust to noise for a family of KS-uncolourable hypergraphs including many known KS constructions, using this method. Indeed, for this family, the problem of obtaining noncontextuality inequalities turns out to be intimately connected to edge covers of graphs.