  In this work we study rank-one quantum games. In particular, we focus on the
study of the computability of the entangled value $\omega^*$. We show that the
value $\omega^*$ can be efficiently approximated up to a multiplicative factor
of 4. We also study the behavior of $\omega^*$ under the parallel repetition of
rank-one quantum games, showing that it does not verify a perfect parallel
repetition theorem. To obtain these results, we first connect rank-one games
with the mathematical theory of operator spaces. We also reprove with these new
tools essentially known results about the entangled value of rank-one games
with one-way communication $\omega_{qow}$. In particular, we show that
$\omega_{qow}$ can be computed efficiently and it satisfies a perfect parallel
repetition theorem.
