A Hierarchy of Efficient Bounds on Quantum Capacities Exploiting Symmetry
| Autor: | Omar Fawzi, Hoang Ta, Ala Shayeghi |
|---|---|
| Přispěvatelé: | Traitement optimal de l'information avec des dispositifs quantiques (QINFO), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Grenoble Alpes (UGA)-Inria Lyon, Institut National de Recherche en Informatique et en Automatique (Inria), European Project: 851716,ERC-2019-STG,AlgoQIP(2021), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Semidefinite programming
Quantum Physics FOS: Physical sciences 020206 networking & telecommunications 02 engineering and technology Quantum channel Library and Information Sciences Computer Science Applications Classical capacity Channel capacity [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] 0202 electrical engineering electronic engineering information engineering Applied mathematics Amplitude damping channel Convex function Divergence (statistics) Quantum Physics (quant-ph) ComputingMilieux_MISCELLANEOUS Quantum computer Mathematics Information Systems Computer Science::Information Theory |
| Zdroj: | IEEE Transactions on Information Theory IEEE Transactions on Information Theory, 2022, 68 (11), pp.7346-7360. ⟨10.1109/TIT.2022.3182101⟩ 2021 IEEE International Symposium on Information Theory (ISIT) 2021 IEEE International Symposium on Information Theory (ISIT), Jul 2021, Melbourne, France. pp.272-277, ⟨10.1109/ISIT45174.2021.9517913⟩ ISIT |
| ISSN: | 0018-9448 |
| DOI: | 10.1109/TIT.2022.3182101⟩ |
| Popis: | Optimal rates for achieving an information processing task are often characterized in terms of regularized information measures. In many cases of quantum tasks, we do not know how to compute such quantities. Here, we exploit the symmetries in the recently introduced $D^{\#}$ in order to obtain a hierarchy of semidefinite programming bounds on various regularized quantities. As applications, we give a general procedure to give efficient bounds on the regularized Umegaki channel divergence as well as the classical capacity and two-way assisted quantum capacity of quantum channels. In particular, we obtain slight improvements for the capacity of the amplitude damping channel. We also prove that for fixed input and output dimensions, the regularized sandwiched R\'enyi divergence between any two quantum channels can be approximated up to an $\epsilon$ accuracy in time that is polynomial in $1/\epsilon$. |
| Databáze: | OpenAIRE |
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