Non-stabilizerness and violations of CHSH inequalities
quant-ph
Submitted: 2025-04-04
Updated: 2026-09-07
Comments: 24 pages, 6 figures, 2 tables
Journal ref: Quantum 10, 2214 (2026)
DOI: 10.22331/q-2026-09-21-2214
License: http://creativecommons.org/licenses/by/4.0/
The gist: We study quantitatively the interplay between entanglement and non-stabilizer resources in violating the CHSH inequalities.
Terminology
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) 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.
Sources
- Witnessing Magic with Bell inequalities
- Stabilizer Codes and Quantum Error Correction
- The Heisenberg Representation of Quantum Computers
- Probes of chaos over the Clifford group and approach to Haar values
- Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems
- Long-range nonstabilizerness and quantum codes, phases, and complexity
- Evaluating many-body stabilizer R'enyi entropy by sampling reduced Pauli strings: singularities, volume law, and nonlocal magic
- Non-Local Magic Resources for Fermionic Gaussian States
- The Clifford group fails gracefully to be a unitary 4-design
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