Classical Limit: Dissipation of Spekkens' Generalised Contextuality under Decoherence

TL;DR

This paper demonstrates how decoherence can cause Spekkens' generalized contextuality in certain quantum systems to diminish, providing insights into the classical-quantum boundary and quantum computational advantage.

Contribution

It shows that decoherence can suppress Spekkens' contextuality in stabiliser systems with magic states, linking decoherence, contextuality, and quantum advantage.

Findings

Decoherence causes Spekkens' contextuality to become noncontextual after a threshold.

Some quasiprobability representations are more effective in witnessing the transition.

The results relate decoherence and contextuality to quantum computational power.

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.