@article{06f194f7f2724e0cadeba18d50be52b1,
title = "On the relation between completely bounded and (1,cb)-summing maps with applications to quantum XOR games",
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 (1,cb)-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 = "Completely bounded maps, Operator spaces, Quantum XOR games, cb-summing maps",
author = "Marius Junge and Kubicki, {Aleksander M.} and Carlos Palazuelos and Ignacio Villanueva",
note = "Funding Information: MJ is partially supported by the NSF grants DMS 1800872 and Raise-TAG183917 . A. M. K is partially supported by the European Research Council (ERC) (grant agreement No 648913 ) and Spanish MICINN project MTM2014-57838-C2-2-P . C.P. is partially supported by the MICINN project PID2020-113523GB-I00 and by QUITEMAD+-CM, P2018/TCS4342 , funded by Comunidad de Madrid . I. V. is partially supported by the MICINN project PID2020-116398GB-I00 . C.P. and I. V. are partially supported by Grant CEX2019-000904-S funded by MCINN/AEI/10.13039/501100011033 . Publisher Copyright: {\textcopyright} 2022 The Author(s)",
year = "2022",
month = dec,
day = "15",
doi = "10.1016/j.jfa.2022.109708",
language = "English (US)",
volume = "283",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "12",
}