Parallel Repetition of Entangled Games with Exponential Decay via the Superposed Information Cost

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" summary

Shows that for games with independent uniform questions, if one-shot entangled value equals 1 − ε then the n-fold entangled value falls exponentially with n, with rate roughly Ω(ε^2/(log K + log L)), so ω(G^n) ≤ exp(−Ω(n ε^2/(log K+log L))). Proof introduces the superposed information cost (SIC), proves SIC ≥ Ω(ε), uses mutual information additivity and a chain rule, and applies Uhlmann theorem* on purifications to show SIC zero implies value one, yielding the exponential decay.

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" chapters (11)

1. 0:00Entangled games introduction
2. 3:11Parallel repetition entangled games
3. 7:27Extra resources in entangled games
4. 10:17Limitations of information cost
5. 13:28Superposed information cost
6. 16:41Superposed cost properties
7. 21:43Superposed cost versus game value
8. 25:22Proof insight with superposed states
9. 28:58Winning strategies from superposed states
10. 30:04Recap and conclusions
11. 32:11Q&A