Abstract

I will give an overview of two recent papers on the generalised notion of noncontextuality due to Spekkens. In the first [1] we show that taking into account transformations imposes a surprisingly rigid structure on noncontextual models of tomographically local theories (such as quantum theory). An example of this rigidity is that the number of ontic states in the noncontextual model must equal the dimension of the operational state space. In the second paper [2] we exploit this structure to classify the noncontextual models of the stabilizer subtheories, finding that there is a unique noncontextual model in odd dimension, and no model at all in even dimension. The unique model in odd dimensions is known as Gross’s discrete Wigner function, which could explain why this representation plays a special role in some forms of quantum computation.

[1] https://arxiv.org/abs/2005.07161

[2] https://arxiv.org/abs/2101.06263