Operator Entanglement from Non-Commutative Symmetries

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.

7 pages, 2 figures

References in corpus (14)

• Quantum entanglement
• Quantum Resource Theories
• Chaos in quantum channels
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• The Resource Theory of Stabilizer Computation
• Stabilizer Rényi entropy
• Quantum entanglement of unitary operators on bi-partite systems
• Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• Resource theory of quantum scrambling
• Stabilizer entropy of quantum tetrahedra
• Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
• Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits
• Deformations of the symmetric subspace of qubit chains