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.
Original language | English (US) |
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Article number | 109708 |
Journal | Journal of Functional Analysis |
Volume | 283 |
Issue number | 12 |
DOIs | |
State | Published - Dec 15 2022 |
Keywords
- Completely bounded maps
- Operator spaces
- Quantum XOR games
- cb-summing maps
ASJC Scopus subject areas
- Analysis