Entangled states from quantum algebra $\mathcal{U}_h (\mathfrak{sl}(2, \mathbb{R}))$

• URL: http://arxiv.org/abs/2506.11686v1
• Date: Fri, 13 Jun 2025 11:30:08 GMT
• Title: Entangled states from quantum algebra $\mathcal{U}_h (\mathfrak{sl}(2, \mathbb{R}))$
• Abstract summary: We discuss the application of the Jordanian quantum algebra $mathcalU_h (mathfraksl (2, mathbbR))$, as a Hopf algebra deformation of the Lie algebra $mathfraksl (2, mathbbR)$, in the context of entanglement properties of quantum states.<n>We construct the associated $h$-deformed Dicke states on $mathfraksl (2, mathbbR)$, comparing them to the $q$-
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We discuss the application of the Jordanian quantum algebra $\mathcal{U}_h (\mathfrak{sl}(2, \mathbb{R}))$, as a Hopf algebra deformation of the Lie algebra $\mathfrak{sl}(2, \mathbb{R})$, in the context of entanglement properties of quantum states. For them, several kind of entanglement measures and fidelities are obtained, parametrized by the deformation parameter $h$. In particular, we construct the associated $h$-deformed Dicke states on $\mathfrak{sl}(2, \mathbb{R})$, comparing them to the $q$-Dicke states obtained from the quantum deformation of the $\mathcal U_q (\mathfrak{sl}(2, \mathbb{R}))$. Moreover, the density matrices of these $h$-deformed Dicke states are compared to the experimental realizations of those of Dicke states. A similar behavior is observed, pointing out that the $h$-deformation could be used to describe noise and decoherence effects in experimental settings.

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