Quantum channel simulation and the channel's smooth max-information
File(s)
Working paper
Author(s)
Fang, Kun
Wang, Xin
Tomamichel, Marco
Berta, Mario
Type
Working Paper
Abstract
We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. Second, we introduce the channel's smooth max-information, which can be seen as a one-shot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel's smooth max-information as the one-shot quantum simulation cost under no-signalling assisted codes, which significantly simplifies the study of channel simulation and provides insights and bounds for the case under entanglement-assisted codes. Third, we derive the asymptotic equipartition property of the channel's smooth max-information; i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem in the presence of no-signalling correlations. Finally, we explore the simulation cost of various quantum channels.
Date Issued
2019-10-01
Citation
2019
Publisher
arXiv
Copyright Statement
© 2019 The Author(s)
Identifier
https://arxiv.org/abs/1807.05354v2
Subjects
Science & Technology
Technology
Computer Science, Information Systems
Engineering, Electrical & Electronic
Computer Science
Engineering
CONVERSE BOUNDS
CAPACITY
COMMUNICATION
PROGRAM
Publication Status
Published