Temperley–Lieb Quantum Channels

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 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)).