Temperley-Lieb quantum channels

TL;DR

This paper introduces and analyzes Temperley-Lieb quantum channels, exploring their properties such as entropy, capacity, degradability, and entanglement characteristics, and compares them with TRO-channels, advancing understanding of quantum symmetries in quantum information.

Contribution

It extends the class of quantum channels derived from quantum group symmetries and investigates their information-theoretic properties, providing new insights and applications in quantum information theory.

Findings

Temperley-Lieb channels exhibit specific entropic and capacity properties.

They can be (anti-)degradable, PPT, and entanglement breaking under certain conditions.

Comparison with TRO-channels reveals structural similarities and differences.

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].