One-shot and asymptotic classical capacity in general physical theories
Abstract
With the recent development of quantum information theory, some attempts exist to construct information theory beyond quantum theory. Here we consider hypothesis testing relative entropy and one-shot classical capacity, that is, the optimal rate of classical information transmitted by using a single channel under a constraint of a certain error probability, in general physical theories where states and measurements are operationally defined. Then we obtain the upper bound of one-shot classical capacity by generalizing the method given by Wang and Renner [Phys. Rev. Lett. 108, 200501 (2012)]. Also, we derive the lower bound of the capacity by showing the existence of a good code that can transmit classical information with a certain error probability. Applying the above two bounds, we prove the asymptotic equivalence between classical capacity and hypothesis testing relative entropy even in any general physical theory.
Keywords
Cite
@article{arxiv.2303.04138,
title = {One-shot and asymptotic classical capacity in general physical theories},
author = {Shintaro Minagawa and Hayato Arai},
journal= {arXiv preprint arXiv:2303.04138},
year = {2024}
}
Comments
7+6 pages, 1 figure. Accepted version for publication in PRA. We fixed typos, improved some explanations, and changed the structure of Chapters 5 and 6. The first sentence on page 5 is modified, adding the references