Quantum deformations of U_h(𝔰𝔩(2,ℝ)). Part I: Fidelity and experimental benchmarking

This work (arXiv:2606.19462) explores the effects of both the standard quantum q-deformation and the non-standard h-deformation of the Hopf algebra U(𝔰𝔩(2,ℝ)) on multi-qubit systems. By constructing the states of a Hilbert space of N qubits through the Clebsch-Gordan coefficients associated with the deformed algebras, we show that these states naturally coincide with the eigenstates of the Hamiltonian of the q- and h-deformed Kittel-Shore models. We compare the resulting deformed states with those typically targeted in quantum information experiments, providing a bridge between algebraic constructions and experimentally relevant quantum resources. Fidelities with respect to the undeformed states are computed to establish how the quantum correlations are affected, both for few-qubit systems (including Dicke and non-Dicke states), and in the macroscopic limit (N→∞) through closed-form formulas derived for arbitrary Dicke states. The results reveal different behaviors between the two deformations. The q-deformation smoothly modifies the states and maintains a residual overlap with the original configurations, while the h-deformation rapidly makes the states orthogonal to their undeformed counterparts. Both models demand a standard N−1 rescaling to preserve fidelity stability in the macroscopic limit.

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