Topological phases are expected to carry enhanced computational power, stemming from the long-range entanglement that characterizes them. Here we investigate whether this advantage is reflected in quantum nonstabilizerness (often called magic), quantified through stabilizer Rényi entropies. We analyze both integrable and nonintegrable one-dimensional models with an exact duality between a symmetry-protected topological phase and a trivial one. Surprisingly, a finite (parameter-dependent) asymmetry appears only when boundary conditions break the duality, and emerges as well in the transverse-field Ising chain, which is topologically trivial. These results complement recent analysis in the literature and show that the total of a state is unable to detect symmetry-protected topological phases, indicating either that a different property is required to capture their unique quantum contribution or that not all forms of long-range entanglement constitute a genuine computational resource.

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• Complex systems
• Quantum correlations in quantum information
• Symmetry protected topological states
• 1-dimensional spin chains
• Quantum spin chains
• Tensor network methods