Ottawa, June 7 - 11, 2021
Non-locality of quantum mechanics is often seen as arising from entanglement, but entanglement and non-locality are not quite the same resource. In this talk we discuss one such discrepancy. Entanglement famously allows for catalysts: there are states that can be used to catalyze an otherwise impossible local transformation. More formally, there are quantum states $\rho_1,\rho_2$ such that no (LOCC-)transformation $\rho_1\to\rho_2$ exists but $\psi\otimes \rho_1$ can be transformed to $\psi\otimes \rho_2$.
In this talk we show that such catalysts do not exist for contextuality nor for non-locality. To do so, we first recap what contextuality and non-locality are as features of correlations, and then discuss what does it mean to transform such correlations to others. This lets us formalize the no-catalysis result, which states that if there is a transformation $d\otimes e\to d\otimes f$, then there is a transformation $e\to f$ as well.