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

DOI10.1088/1751-8113/44/41/415306zbMATH Open1251.81022arXiv1103.0286OpenAlexW3098016880MaRDI QIDQ3095458

Tomas Jochym-O'Connor, Kamil Brádler, Mark M. Wilde

Publication date: 2 November 2011

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1103.0286

Mathematics Subject Classification ID

Methods of quantum field theory in general relativity and gravitational theory (83C47) Channel models (including quantum) in information and communication theory (94A40) Quantum state estimation, approximate cloning (81P50) Quantum coding (general) (81P70)