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Mathematical Physics

arXiv:1810.08001 (math-ph)
[Submitted on 18 Oct 2018]

Title:Temperley-Lieb quantum channels

Authors:Michael Brannan, Benoît Collins, Hun Hee Lee, Sang-Gyun Youn
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Abstract:We study a class of quantum channels arising from the representation theory of compact quantum groups that we call Temperley-Lieb quantum channels. These channels simultaneously extend those introduced in [BC18], [AN14], and [LS14]. (Quantum) Symmetries in quantum information theory arise naturally from many points of view, providing an important source of new examples of quantum phenomena, and also serve as useful tools to simplify or solve important problems. This work provides new applications of quantum symmetries in quantum information theory. Among others, we study entropies and capacitites of Temperley-Lieb channels, their (anti-)degradability, PPT and entanglement breaking properties, as well as the behaviour of their tensor products with respect to entangled inpurs. Finally we compare the Tempereley-Lieb channels with the (modified) TRO-channels recently introduced in [GJL16].
Comments: 35 pages
Subjects: Mathematical Physics (math-ph); Operator Algebras (math.OA); Quantum Algebra (math.QA)
MSC classes: 46N50, 47L90, 81P45, 20G42
Cite as: arXiv:1810.08001 [math-ph]
  (or arXiv:1810.08001v1 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1810.08001
Journal reference: Commun. Math. Phys. 376, 795--839 (2020)
Related DOI: https://doi.org/10.1007/s00220-020-03731-2

Submission history

From: Sang-Gyun Youn [view email]
[v1] Thu, 18 Oct 2018 11:53:35 UTC (35 KB)
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