quantum-computing

Non-stabilizerness and violations of CHSH inequalities

Stefano Cusumano, Lorenzo Campos Venuti, Simone Cepollaro, Immacolata De Simone, Gianluca Esposito, Daniele Iannotti, Barbara Jasser, Jovan Odavić, Michele Viscardi, and Alioscia Hamma

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AbstractWe 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.► BibTeX data@article{Cusumano2026nonstabilizerness, doi = {10.22331/q-2026-09-21-2214}, url = {https://doi.org/10.22331/q-2026-09-21-2214}, title = {Non-stabilizerness and violations of {CHSH} inequalities}, author = {Cusumano, Stefano and Campos Venuti, Lorenzo and Cepollaro, Simone and De Simone, Immacolata and Esposito, Gianluca and Iannotti, Daniele and Jasser, Barbara and Odavi{\'{c}}, Jovan and Viscardi, Michele and Hamma, Alioscia}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2214}, month = sep, year = {2026} }► References [1] John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 23: 880–884, Oct 1969. 10.1103/PhysRevLett.23.880. URL https://link.aps.org/doi/10.1103/PhysRevLett.23.880. https://doi.org/10.1103/PhysRevLett.23.880 [2] Mark Howard. Maximum nonlocality and minimum uncertainty using magic states. Phys. Rev. A, 91: 042103, Apr 2015. 10.1103/PhysRevA.91.042103. URL https://link.aps.org/doi/10.1103/PhysRevA.91.042103. https://doi.org/10.1103/PhysRevA.91.042103 [3] Mark Howard, Joel Wallman, Victor Veitch, and Joseph Emerson. Contextuality supplies the ‘magic’ for quantum computation. Nature, 510 (7505): 351–355, 2014. ISSN 1476-4687. 10.1038/nature13460. URL https://doi.org/10.1038/nature13460. https://doi.org/10.1038/nature13460 [4] Mark Howard and Jiri Vala. Nonlocality as a benchmark for universal quantum computation in ising anyon topological quantum computers. Phys. Rev. A, 85: 022304, Feb 2012. 10.1103/PhysRevA.85.022304. URL https://link.aps.org/doi/10.1103/PhysRevA.85.022304. https://doi.org/10.1103/PhysRevA.85.022304 [5] Rafael A. Macedo, Patrick Andriolo, Santiago Zamora, Davide Poderini, and Rafael Chaves. Witnessing magic with bell inequalities, 2025. URL https://arxiv.org/abs/2503.18734. arXiv:2503.18734 [6] Paweł Cieśliński, Lukas Knips, Harald Weinfurter, and Wiesław Laskowski. No-cost bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing. Phys. Rev. A, 113: 052404, May 2026. 10.1103/1nkl-sphd. URL https://link.aps.org/doi/10.1103/1nkl-sphd. https://doi.org/10.1103/1nkl-sphd [7] Daniel Gottesman. Stabilizer Codes and Quantum Error Correction. PhD thesis, Caltech, Pasadena, May 1997. URL http://arxiv.org/abs/quant-ph/9705052. arXiv:quant-ph/9705052. arXiv:quant-ph/9705052 [8] Daniel Gottesman.

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AbstractWe 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.► BibTeX data@article{Cusumano2026nonstabilizerness, doi = {10.22331/q-2026-09-21-2214}, url = {https://doi.org/10.22331/q-2026-09-21-2214}, title = {Non-stabilizerness and violations of {CHSH} inequalities}, author = {Cusumano, Stefano and Campos Venuti, Lorenzo and Cepollaro, Simone and De Simone, Immacolata and Esposito, Gianluca and Iannotti, Daniele and Jasser, Barbara and Odavi{\'{c}}, Jovan and Viscardi, Michele and Hamma, Alioscia}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2214}, month = sep, year = {2026} }► References [1] John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. 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