2026/07/20 by Alejandro Borda Kuhlmann, Julian Rincon
#quant-ph #cond-mat.stat-mech
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.