English

One-shot and asymptotic classical capacity in general physical theories

Quantum Physics 2024-06-14 v3

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