The Sachdev-Ye-Kitaev (SYK) model is of paramount importance for the understanding of both strange metals and a microscopic theory of two-dimensional gravity. We study the interplay between stabilizer Rényi entropy and entanglement entropy in both the ground state and highly excited states of the $\mathrm{SYK}-4+\mathrm{SYK}-2$ model, interpolating the highly chaotic four-body interactions model with the integrable two-body interactions one. The interplay between these quantities is also assessed through universal statistics of the entanglement spectrum and its antiflatness. We find that SYK-4 is indeed characterized by a complex pattern of both entanglement and nonstabilizer resources, while SYK-2 is nonuniversal and not complex. We discuss the fragility and robustness of these features depending on the interpolation parameter.

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• Quantum chaos
• Quantum correlations in quantum information
• Quantum entanglement
• Resource theories
• Sachdev-Ye-Kitaev model