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arXiv · 2504.03351

Non-stabilizerness and violations of CHSH inequalities

Stefano Cusumano·Lorenzo Campos Venuti·Simone Cepollaro·Immacolata De Simone·Gianluca Esposito·Daniele Iannotti·Barbara Jasser·Jovan Odavi\' c·Michele Viscardi·Alioscia Hamma
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Abstract

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) {\it 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.

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Stefano Cusumano, Lorenzo Campos Venuti, Simone Cepollaro, Immacolata De Simone, Gianluca Esposito, Daniele Iannotti, Barbara Jasser, Jovan Odavi\' c, Michele Viscardi, Alioscia Hamma. 2025-04-04. Non-stabilizerness and violations of CHSH inequalities. https://arxiv.org/abs/2504.03351

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