To violate CHSH inequalities, quantum magic must be asymmetric and local.

Quantum physics allows particles to share connections that defy everyday rules. Tests called CHSH inequalitiesCHSH inequalitiesA specific Bell inequality that detects quantum nonlocality beyond classical possibilities. measure this behavior. To break standard limits, systems must rely on entanglement and special ingredients called non-stabilizer resources. Entanglement links particles together, while non-stabilizer resources provide the extra complexity needed for quantum power. Researchers studied how these two elements work together. They found that non-stabilizer resources are strictly required to violate the inequality. Surprisingly, these resources must be local to individual parts rather than spread out, and they must be asymmetric. The team used a tool called stabilizer entropystabilizer entropyAn entropy-like quantity that quantifies the amount of non-stabilizer (magic) in a quantum state. to measure these ingredients and track violation odds. They also examined the flatness of the entanglement spectrumentanglement spectrumThe set of eigenvalues of the reduced density matrix, describing how entanglement is distributed across a bipartite system.. Using these findings, they designed a method to assemble states that break the rules more reliably.

Why it matters

Testing nonlocality with Bell inequalities is a core diagnostic for quantum technology. This work reveals that non-stabilizer 'magic' — the very resource that gives quantum computers power — must be arranged in a specific way to violate these tests. The finding sharpens our understanding of what makes quantum entanglement actually useful for tasks like secure communication.

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