Abstract
In this work, we study rank-one quantum games. In particular, we focus on the study of the computability of the entangled value ω*. We show that the value ω* can be efficiently approximated up to a multiplicative factor of 4. We also study the behavior of ω* 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 ω qow . In particular, we show that ω qow can be computed efficiently and it satisfies a perfect parallel repetition theorem.
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Cooney, T., Junge, M., Palazuelos, C. et al. Rank-one quantum games. comput. complex. 24, 133–196 (2015). https://doi.org/10.1007/s00037-014-0096-x
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DOI: https://doi.org/10.1007/s00037-014-0096-x