Classical Limit: Dissipation of Spekkens' Generalised Contextuality under Decoherence

Abstract

Contextuality is considered as one of the most distinctive features of nonclassical systems. Here, we show that a Spekkens contextual system (which previous work has shown is a necessary condition for nonclassicality) formed of an odd-dimensional stabiliser system plus a magic state becomes noncontextual (a sufficient condition for classicality) under the action of a depolarising channel after a certain decoherence threshold. We show also that some quasiprobability representations are more effective than others in witnessing this transition from contextuality to noncontextuality. Given previous work has shown that magic states and Spekkens contextuality are both necessary for universal quantum computation, this result helps us understand the relationship between decoherence, Spekkens' generalised contextuality, and quantum advantage.