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

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.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2607.18400 [quant-ph]

(or arXiv:2607.18400v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.18400 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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