We argue that Hopf-algebra deformations of symmetries—as encountered in noncommutative models of quantum spacetime—carry an intrinsic content of operator entanglement that is enforced by the coproduct-defined notion of composite generators. As a minimal and exactly solvable example, we analyze the $U_q(\mathfrak{su}(2))$ quantum group and a two-qubit realization obtained from the coproduct of a $q$-deformed single-spin Hamiltonian. Although the deformation is invisible on a single qubit, it resurfaces in the two-qubit sector through the non-cocommutative coproduct, yielding a family of intrinsically nonlocal unitaries. We compute their operator entanglement in closed form and show that, for Haar-uniform product inputs, their entangling power is fully determined by the latter. This provides a concrete mechanism by which noncommutative symmetries enforce a baseline of entanglement at the algebraic level, with implications for information dynamics in quantum-spacetime settings and quantum information processing.

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• Entanglement production
• Nonlocality
• Quantum information theory