University of York, UK, matthew.pusey@york.ac.uk
(joint work with John Selby, David Schmid, and Rob Spekkens)
A well-motivated criteria for classicality is the existence of a noncontextual ontological model [1]. Existing work on such models has mostly considered preparations and measurements, with much less attention paid to transformations. I will diagrammatically prove a structure theorem [2] about the representation of transformations in noncontextual ontological models of locally tomographic operational theories (including quantum theory). One striking consequence of this theorem is a severe restriction on the number of ontic states in the model. For example, a noncontextual model of a qubit could have at most four ontic states. Combining this with the fact that any ontological model of a qubit must in fact have an infinite number of ontic states immediately gives a new proof that qubits do not admit a noncontextual model. Time permitting, I will mention an analogous structure theorem regarding quasiprobability representations [3] and a recent application [4] of our structure theorem to the stabilizer formalism.
[1] R. W. Spekkens. Contextuality for preparations, transformations, and unsharp measurements. Phys. Rev. A 71, 052108 (2005).
[2] D. Schmid, J. H. Selby, M. F. Pusey, and R. W. Spekkens. A structure theorem for generalized-noncontextual ontological models. arXiv:2005.07161 (2020).
[3] C. Ferrie, Quasi-probability representations of quantum theory with applications to quantum information science. Rep. Prog. Phys. 74, 116001 (2011).
[4] D. Schmid, H. Du, J. H. Selby, and M. F. Pusey, The only noncontextual model of the stabilizer subtheory is Gross’s. arXiv:2101.06263 (2021).