Observable bound on ontic disturbance in the qubit contextuality test

Derive a bound on the ontic disturbance parameter $p_d$ solely from observable statistics for the specific qubit-pointer instrument defined by the weak coupling $U_\theta=e^{-i\theta\mathcal{E}\otimes\sigma_z}$.

Background

The qubit-pointer contextuality inequality depends on an ontological nondisturbance parameter $p_d$, which bounds how much the readout changes post-selection probabilities at the ontic level. The paper proves that the experimentally observable nonselective disturbance is second order in the coupling, but this does not itself provide an observable upper bound on the ontic quantity required by the noncontextuality argument.

The authors explicitly state that obtaining such a bound remains unresolved for the particular instrument used in the proposed experiment.