Quantum Wasserstein distances for quantum permutation groups

Fuente: arXiv
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Autori principali: Anshu, Jekel, David, Landry, Therese Basa
Natura: Preprint
Pubblicazione: 2025
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author Anshu
Jekel, David
Landry, Therese Basa
author_facet Anshu
Jekel, David
Landry, Therese Basa
contents We seek an analog for the quantum permutation group $S_n^+$ of the normalized Hamming distance for permutations. We define three distances on the tracial state space of $C(S_n^+)$ that generalize the $L^1$-Wasserstein distance of probability measures on $S_n$ equipped with the normalized Hamming metric, for which we demonstrate basic metric properties, subadditivity under convolution, and density of the Lipschitz elements in the $\mathrm{C}^{\ast}$-algebra.
format Preprint
id arxiv_https___arxiv_org_abs_2505_19269
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quantum Wasserstein distances for quantum permutation groups
Anshu
Jekel, David
Landry, Therese Basa
Operator Algebras
Primary: 46L67, 49Q22, Secondary: 46L89, 81R60
We seek an analog for the quantum permutation group $S_n^+$ of the normalized Hamming distance for permutations. We define three distances on the tracial state space of $C(S_n^+)$ that generalize the $L^1$-Wasserstein distance of probability measures on $S_n$ equipped with the normalized Hamming metric, for which we demonstrate basic metric properties, subadditivity under convolution, and density of the Lipschitz elements in the $\mathrm{C}^{\ast}$-algebra.
title Quantum Wasserstein distances for quantum permutation groups
topic Operator Algebras
Primary: 46L67, 49Q22, Secondary: 46L89, 81R60
url https://arxiv.org/abs/2505.19269