Geodesic
Limit Formulas for the Trace of the Functional Calculus of Quantum Channels for SU(2)
Robin Van Haastrecht1, 2, 3, 4, 5
1Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg University, Gothenburg, Sweden
2In 2014 Lieb and Solovej studied traces of quantum channels, which are defined by the leading component in the decomposition of the tensor product of two irreducible representations of SU(2), to establish a Wehrl-type inequality for integrals of convex functions of matrix coefficients. It is proved that the integral is the limit of the trace of the functional calculus of quantum channels. In this paper, we introduce new quantum channels for all the components in the tensor product and generalize their limit formula. We prove that the limit can be expressed using Berezin transforms.
3Keywords: Quantum channels, reproducing kernels, Hermitian symmetric spaces, limit formulas, Wehrl inequality.
4MSC: 22E46, 47B38, 81P47.
5[
Journal of Lie Theory, Tome 34 (2024) no. 3, pp. 653-676

Voir la notice de l'article provenant de la source Heldermann Verlag

In 2014 Lieb and Solovej studied traces of quantum channels, which are defined by the leading component in the decomposition of the tensor product of two irreducible representations of SU(2), to establish a Wehrl-type inequality for integrals of convex functions of matrix coefficients. It is proved that the integral is the limit of the trace of the functional calculus of quantum channels. In this paper, we introduce new quantum channels for all the components in the tensor product and generalize their limit formula. We prove that the limit can be expressed using Berezin transforms.
Classification : 22E46, 47B38, 81P47
Mots-clés : Quantum channels, reproducing kernels, Hermitian symmetric spaces, limit formulas, Wehrl inequality

Robin Van Haastrecht  1 , 2 , 3 , 4 , 5

1 Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg University, Gothenburg, Sweden
2 In 2014 Lieb and Solovej studied traces of quantum channels, which are defined by the leading component in the decomposition of the tensor product of two irreducible representations of SU(2), to establish a Wehrl-type inequality for integrals of convex functions of matrix coefficients. It is proved that the integral is the limit of the trace of the functional calculus of quantum channels. In this paper, we introduce new quantum channels for all the components in the tensor product and generalize their limit formula. We prove that the limit can be expressed using Berezin transforms.
3 Keywords: Quantum channels, reproducing kernels, Hermitian symmetric spaces, limit formulas, Wehrl inequality.
4 MSC: 22E46, 47B38, 81P47.
5 [ 
Robin Van Haastrecht. Limit Formulas for the Trace of the Functional Calculus of Quantum Channels for SU(2). Journal of Lie Theory, Tome 34 (2024) no. 3, pp. 653-676. http://geodesic.mathdoc.fr/item/JOLT_2024_34_3_a8/
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     author = {Robin Van Haastrecht},
     title = {Limit {Formulas} for the {Trace} of the {Functional} {Calculus} of {Quantum} {Channels} for {SU(2)}},
     journal = {Journal of Lie Theory},
     pages = {653--676},
     year = {2024},
     volume = {34},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2024_34_3_a8/}
}
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