An Infinite Sequence of Additive Channels: the Classical Capacity of Cloning Channels

TL;DR

This paper introduces an infinite sequence of quantum channels related to cloning machines, demonstrating their additive Holevo capacity and providing new insights into classical and quantum capacity calculations.

Contribution

It presents a novel infinite series of channels with proven additivity of the Holevo capacity, including an example of an infinite-dimensional channel with easily computable capacities.

Findings

Proved additivity of Holevo capacity for the channel series

Connected the channels to universal quantum cloning machines

Provided a method to compute capacities for certain infinite-dimensional channels

Abstract

We introduce an infinite sequence of quantum channels for which the Holevo capacity is additive. The channel series is closely related to the quantum channels arising from universal quantum cloning machines. The additivity proof is motivated by a special property the studied channels enjoy: the property of conjugate degradability. As a consequence of the announced proof, we also provide an easy way of proving the additivity of the Holevo capacity for the original Unruh channel for which the quantum capacity is already known. Consequently, we present not only an infinite series of finite-dimensional channels but also a nontrivial example of an infinite-dimensional channel for which the classical and quantum channel capacities are easily calculable.