Optimal quantum preparation contextuality in $n$-bit parity-oblivious multiplexing task

Understand

In [ PRL, 102, 010401 (2009)], Spekkens et al., have shown that quantum preparation contextuality can power the parity-oblivious multiplexing (POM) task.

• The bound on the optimal success probability of $n$-bit POM task performed with the classical resources was shown to be the \textit{same} as in a preparation non-contextual theory.
• This non-contextual bound is violated if the task is performed with quantum resources.
• While in $2$-bit POM task the optimal quantum success probability is achieved, in 3-bit case optimality was left as an open question.