Conjugate degradable channels: A new class of quantum channels with a tractable quantum capacity formula

TL;DR

This paper introduces the first example of conjugate degradable quantum channels that are not degradable, providing a new class with a tractable quantum capacity formula and linking them to optimal universal asymmetric cloning.

Contribution

It presents the first non-degradable conjugate degradable channels and establishes their physical origin as optimal asymmetric cloners, expanding the understanding of quantum channel capacities.

Findings

First example of non-degradable conjugate degradable channels

Quantum capacity of optimal asymmetric 1->1+1 cloning channels calculated

Conjugate degradable channels form a new class with a single-letter capacity formula

Abstract

Conjugate degradable channels are channels whose quantum capacity is calculable. They were defined and studied in [1] where, however, only channels that are both degradable and conjugate degradable were found. In this paper we bring the very first example of conjugate degradable channels that are not degradable. We also identify the physical origin of these channels and show that they belong to the class of optimal universal asymmetric cloners. We thus not only positively answer the question whether conjugate degradable channels form a new class of channels with a single-letter capacity formula but as a side result we also calculate the quantum capacity of the optimal asymmetric 1->1+1 cloning channels.