Neither Contextuality nor Nonlocality Admits Catalysts

TL;DR

This paper proves that neither contextuality nor nonlocality can be enhanced through catalysts in resource transformations, highlighting a fundamental difference from entanglement behavior.

Contribution

It establishes that resource theories of contextuality and nonlocality do not admit catalysts, unlike entanglement, revealing key distinctions among quantum resources.

Findings

Resource theory of contextuality admits no catalysts.

Nonlocality also does not admit catalysts.

Catalysis remains impossible even with enhanced free operations.

Abstract

We show that the resource theory of contextuality does not admit catalysts, i.e., there are no correlations that can enable an otherwise impossible resource conversion and still be recovered afterward. As a corollary, we observe that the same holds for nonlocality. As entanglement allows for catalysts, this adds a further example to the list of "anomalies of entanglement," showing that nonlocality and entanglement behave differently as resources. We also show that catalysis remains impossible even if, instead of classical randomness, we allow some more powerful behaviors to be used freely in the free transformations of the resource theory.