Determine the optimal noisy parallel-repetition exponent

Determine whether the exponential base in the noisy parallel repetition theorem for the CHSH game is strictly less than the noiseless quantum value \(\cos^2(\pi/8)\) for every noise level, whether this holds for maximal correlation above \(0.36\), and whether the base for a general non-local game converges to its classical parallel-repetition rate \(w_G\) once the shared noisy states become unentangled.

Background

The paper proves noisy parallel repetition bounds for general games and sharper bounds for unique games, including CHSH. For CHSH, the resulting exponential base is smaller than the noiseless quantum value only up to maximal correlation $0.36$, while the authors expect stronger behavior at higher noise levels. The authors also note that their bounds do not exactly recover the classical rate when the noisy states are already unentangled, even though the noisy value should then coincide with the classical value.

References

We suspect that the base of the exponent for CHSH for example, should be lower than \cos2(\pi/8) for any noise level, and this certainly should be true for noise levels that lead to maximal correlation above 0.36.

— Non-local games and communication complexity with noisy entanglement  (2609.05122 - Kundu et al., 4 Sep 2026) in Section 5, subsection “Open problems,” first bullet

There may be an extension of their result that is of the correct form to work with our techniques.

— Non-local games and communication complexity with noisy entanglement  (2609.05122 - Kundu et al., 4 Sep 2026) in Section 5, subsection “Open problems,” second bullet

Perhaps a measure such as the maximal entanglement introduced by Beigi could be useful here.

— Non-local games and communication complexity with noisy entanglement  (2609.05122 - Kundu et al., 4 Sep 2026) in Section 5, subsection “Open problems,” third bullet