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 by Brannan and Collins (Commun Math Phys 358(3):1007–1025, 2018), Nuwairan (Int J Math 25(6):1450048, 2014) and Lieb and Solovej (Acta Math 212(2):379–398, 2014). (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 by Gao et al. (Commun Math Phys 364(1):83–121, 2018)).

中文翻译：

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Temperley-Lieb 量子通道

我们研究了一类由紧凑量子群的表示理论产生的量子通道，我们称之为 Temperley-Lieb 量子通道。这些通道同时扩展了 Brannan 和 Collins (Commun Math Phys 358(3):1007–1025, 2018)、Nuwairan (Int J Math 25(6):1450048, 2014) 和 Lieb 和 Solovej (Acta Math 212(2) ):379–398, 2014)。量子信息论中的（量子）对称性从许多角度自然产生，提供了量子现象新例子的重要来源，也可作为简化或解决重要问题的有用工具。这项工作提供了量子对称性在量子信息理论中的新应用。其中，我们研究了 Temperley-Lieb 通道的熵和容量、它们的（抗）降解性、PPT 和缠结断裂特性，以及它们的张量积关于纠缠的 inpur 的行为。最后，我们将 Tempereley-Lieb 通道与 Gao 等人最近引入的（修改后的）TRO 通道进行了比较。(Commun Math Phys 364(1):83–121, 2018))。