Conjugate Degradability and the Quantum Capacity of Cloning Channels

TL;DR

This paper introduces conjugate degradability, a property that simplifies quantum capacity calculation for certain channels, and applies it to compute capacities of universal cloning machines and an accelerating receiver channel.

Contribution

It defines conjugate degradability, explores its properties, and calculates quantum capacities for specific channels, including universal cloning and an accelerating receiver channel.

Findings

All channels studied have strictly positive quantum capacity.

Conjugate degradability allows single-letter capacity formulas.

Capacities of universal cloning machines are explicitly computed.

Abstract

A quantum channel is conjugate degradable if the channel's environment can be simulated up to complex conjugation using the channel's output. For all such channels, the quantum capacity can be evaluated using a single-letter formula. In this article we introduce conjugate degradability and establish a number of its basic properties. We then use it to calculate the quantum capacity of N to N+1 and 1 to M universal quantum cloning machines as well as the quantum capacity of a channel that arises naturally when data is being transmitted to an accelerating receiver. All the channels considered turn out to have strictly positive quantum capacity, meaning they could be used as part of a communication system to send quantum states reliably.