# How can one define contextuality within the circuit model?

It is in general believed that contextuality is one of the quantum resource that provides the quantum advantage. A context is usually defined in terms of a set of commuting observables. The quantum algorithms are usually describe employing the circuit model. I am curious how can one define contextuality in the within the circuit model?

To be concrete, we may consider Peres-Mermin Square and define a circuit representing each observable at each spot. I think the above definition of contextuality require some upgrading while combining all the gates to implement quantum contextuality for Peres-Mermin square. Please share any suggestion or any reference that can be help as a starting point.

Spekken (2005) generalizes the above definition of contextuality. Could we apply Spekken definition for a circuit model too?

That being said, such a model has been considered in this paper and is called the $$C^*$$-circuit model.