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arXiv:2512.24806 · Physical review. D/Physical review. D.

Operator Entanglement from Non-Commutative Symmetries

Michele Arzano, Goffredo Chirco

quant-phgr-qchep-thSubmitted Dec 31, 2025• Announced Jan 1, 2026• 0 citations
arXivHTMLPDF

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.

DOI
10.1103/kk84-tvfj
Comments
7 pages, 2 figures

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