Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks

Generalized contextuality is the 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, robustness of contextuality to depolarization as well as a minimization of 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 depolarization 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.