Non-stabilizerness and violations of CHSH inequalities

Quantum 10, 2214 (2026).

https://doi.org/10.22331/q-2026-09-21-2214

We study quantitatively the interplay between entanglement and non-stabilizer resources in violating the CHSH inequalities. We show that, while non-stabilizer resources are necessary, they must have a specific structure, namely they need to be both asymmetric and (surprisingly) $textit{local}$. We employ stabilizer entropy (SE) to quantify the non-stabilizer resources involved and the probability of violation given the resources. We show how spectral quantities related to the flatness of entanglement spectrum and its relationship with non-local SE affect the CHSH inequality. Finally, we utilize these results – together with tools from representation theory – to construct a systematic way of building ensembles of states with higher probability of violation.