On the relation between completely bounded and $(1,cb)$-summing maps with applications to quantum XOR games
Functional Analysis
2023-02-24 v1 Quantum Physics
Abstract
In this work we show that, given a linear map from a general operator space into the dual of a C-algebra, its completely bounded norm is upper bounded by a universal constant times its -summing norm. This problem is motivated by the study of quantum XOR games in the field of quantum information theory. In particular, our results imply that for such games entangled strategies cannot be arbitrarily better than those strategies using one-way classical communication.
Keywords
Cite
@article{arxiv.2112.05214,
title = {On the relation between completely bounded and $(1,cb)$-summing maps with applications to quantum XOR games},
author = {Marius Junge and Aleksander M. Kubicki and Carlos Palazuelos and Ignacio Villanueva},
journal= {arXiv preprint arXiv:2112.05214},
year = {2023}
}