  Generalised contextuality is a well-motivated notion of nonclassicality
powering up a myriad of quantum tasks, among which is the celebrated case of a
two-party information processing task where classical information is compressed
in a quantum channel, the parity-oblivious multiplexing (POM) task. The success
rate is the standard quantifier of resourcefulness for this task, while
robustness-based quantifiers are as operationally motivated and have known
general properties. In this work, we leverage analytical and numerical tools to
estimate robustness of contextuality in POM scenarios under different types of
noise. We conclude that for the 3-to-1 case the robustness of contextuality to
depolarisation, as well as a minimisation of the robustness of contextuality to
dephasing over all bases, are good quantifiers for the nonclassical advantage
of this scenario. Moreover, we obtain a general relation between robustness of
contextuality to depolarisation and the success rate in any $n$-to-1 POM
scenario and show how it can be used to bound the number of bits encoded in
this task.
