Magic-protected entanglement and Clifford-irreducible structure in magic state space

• URL: http://arxiv.org/abs/2607.18400v1
• Date: Mon, 20 Jul 2026 18:00:20 GMT
• Title: Magic-protected entanglement and Clifford-irreducible structure in magic state space
• Abstract summary: We develop a Clifford-orbit framework for studying magic-protected entanglement.<n>It defines canonical representatives, spectra, and ranks that characterize the Clifford-irreducible structure of a state.<n>These results identify magical entanglement as an orbit-level diagnostic of how nonstabilizerness protects quantum correlations against Clifford reduction.
• Score: 45.88028371034407
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a Clifford-orbit framework for studying magic-protected entanglement, which we refer to as magical entanglement: the part of bipartite entanglement that remains after optimal stabilizer simplification. This construction leverages residual entanglement under Clifford reduction as a state-level organizing principle for magic state space. It defines canonical representatives, spectra, and ranks that characterize the Clifford-irreducible structure of a state. We identify two regimes of the magic-entanglement interplay. In the $T$-magic regime, local nonstabilizer resources can coexist with entanglement, but the protected component remains weak and state-dependent. In the $W$-magic regime, by contrast, entanglement is Clifford-irreducibly tied to nonstabilizerness, producing typical, strongly self-averaging behavior. Analytical examples and random-circuit numerics support a crossover from broad $T$-magic fluctuations to concentrated, Haar-like $W$-magic behavior. These results identify magical entanglement as an orbit-level diagnostic of how nonstabilizerness protects quantum correlations against Clifford reduction.

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