On the relation between completely bounded and (1, cb)- summing maps with applications to quantum xor games

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Junge, Marius and Kubicki, Alexander M. and Palazuelos Cabezón, Carlos and Villanueva, Ignacio (2022) On the relation between completely bounded and (1, cb)- summing maps with applications to quantum xor games. Journal of Functional Analysis, 283 (12). ISSN 0022-1236

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Official URL: https://doi.org/10.1016/j.jfa.2022.109708



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.


Item Type:Article
Additional Information:

CRUE-CSIC (Acuerdos Transformativos 2022)

Uncontrolled Keywords:Operator spaces; Completely bounded maps; Cb-summing maps; Quantum XOR games
Subjects:Sciences > Physics > Quantum theory
Sciences > Mathematics > Functional analysis and Operator theory
ID Code:73513
Deposited On:11 Jul 2022 16:13
Last Modified:21 Nov 2022 09:40

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