Quantum deformations of $\mathcal{U}(\mathfrak{sl}(2, \mathbb{R}))$. Part I: Fidelity and experimental benchmarking

• URL: http://arxiv.org/abs/2606.19462v1
• Date: Wed, 17 Jun 2026 18:01:20 GMT
• Title: Quantum deformations of $\mathcal{U}(\mathfrak{sl}(2, \mathbb{R}))$. Part I: Fidelity and experimental benchmarking
• Abstract summary: This work explores the effects of the standard quantum $q$-deformation and the non-standard $h$-deformation on multi-qubit systems.<n>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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work explores the effects of both the standard quantum $q$-deformation and the non-standard $h$-deformation of the Hopf algebra $\mathcal{U}(\mathfrak{sl}(2, \mathbb{R}))$ 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 ($N \to \infty$) 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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