Trade-off coding for universal qudit cloners motivated by the Unruh effect

TL;DR

This paper analyzes the capacity regions of the d-dimensional Unruh quantum channel, showing it is tractable and related to universal qudit cloning, with larger achievable rate sets than time-sharing strategies.

Contribution

It identifies the Unruh channel as belonging to a class with single-use capacity optimization and explicitly determines its quantum and private dynamic capacity regions.

Findings

Capacity regions are explicitly calculated for the Unruh channel.

The achievable rate set exceeds that of time-sharing strategies.

The Unruh channel is structurally linked to universal qudit cloning.

Abstract

A "triple trade-off" capacity region of a noisy quantum channel provides a more complete description of its capabilities than does a single capacity formula. However, few full descriptions of a channel's ability have been given due to the difficult nature of the calculation of such regions---it may demand an optimization of information-theoretic quantities over an infinite number of channel uses. This work analyzes the d-dimensional Unruh channel, a noisy quantum channel which emerges in relativistic quantum information theory. We show that this channel belongs to the class of quantum channels whose capacity region requires an optimization over a single channel use, and as such is tractable. We determine two triple-trade off regions, the quantum dynamic capacity region and the private dynamic capacity region, of the d-dimensional Unruh channel. Our results show that the set of achievable rate triples using this coding strategy is larger than the set achieved using a time-sharing strategy. Furthermore, we prove that the Unruh channel has a distinct structure made up of universal qudit cloning channels, thus providing a clear relationship between this relativistic channel and the process of stimulated emission present in quantum optical amplifiers.