Operator Entanglement from Non-Commutative Symmetries

• URL: http://arxiv.org/abs/2512.24806v1
• Date: Wed, 31 Dec 2025 11:49:25 GMT
• Title: Operator Entanglement from Non-Commutative Symmetries
• Authors: Michele Arzano, Goffredo Chirco,
• Abstract summary: We argue that Hopf-algebra deformations of symmetries carry an intrinsic content of $operator$ $entanglement$ that is enforced by the coproduct-defined notion of composite generators.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We argue that Hopf-algebra deformations of symmetries -- as encountered in non-commutative 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 non-commutative 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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