# The non-disjoint ontic states of the Grassmann ontological model, transformation contextuality, and the single qubit stabilizer subtheory

We show that it is possible to construct a preparation non-contextual ontological model that does
not exhibit ‘transformation contextuality’ for single qubits in the stabilizer subtheory. In
particular, we consider the ‘blowtorch’ map and show that it does not exhibit transformation
contextuality under the Grassmann Wigner–Weyl–Moyal (WWM) qubit formalism. Furthermore, the
transformation in this formalism can be fully expressed at order ##IMG##
[http://ej.iop.org/images/1751-8121/52/9/095303/aaafca7ieqn001.gif] , where it satisfies all of
Kolmogorov’s axioms of classical probability theory, and so does not qualify as a candidate quantum
phenomenon. In particular, we find that the Grassmann WWM formalism at order ##IMG##
[http://ej.iop.org/images/1751-8121/52/9/095303/aaafca7ieqn002.gif] corresponds to an ontological
model governed by an additional set of constraints arising from the relations defining the Grassmann
algebra. Due to...