ECCC-Report TR16-060https://eccc.weizmann.ac.il/report/2016/060Comments and Revisions published for TR16-060en-usFri, 15 Apr 2016 12:25:50 +0300
Paper TR16-060
| A parallel repetition theorem for all entangled games |
Henry Yuen
https://eccc.weizmann.ac.il/report/2016/060 The behavior of games repeated in parallel, when played with quantumly entangled players, has received much attention in recent years. Quantum analogues of Raz's classical parallel repetition theorem have been proved for many special classes of games. However, for general entangled games no parallel repetition theorem was known.
We prove that the entangled value of a two-player game $G$ repeated $n$ times in parallel is at most $c_G n^{-1/4} \log n$ for a constant $c_G$ depending on $G$, provided that the entangled value of $G$ is less than $1$. In particular, this gives the first proof that the entangled value of a parallel repeated game must converge to $0$ for *all* games whose entangled value is less than $1$. Central to our proof is a combination of both classical and quantum correlated sampling.Fri, 15 Apr 2016 12:25:50 +0300https://eccc.weizmann.ac.il/report/2016/060