  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.

Functional Analysis;Quantum Physics