Establish a tight key-rate comparison for Parity Magic Square and related protocols

Establish a tight comparison of the key rates achieved by the Parity Magic Square game, the Parity-CHSH game, and the Parallel Parity-CHSH game, including the unresolved entropy bounds needed to evaluate the latter protocol.

Background

The paper introduces the Parallel Parity-CHSH game as a possible benchmark for comparing the Parity Magic Square protocol with parallel two-party device-independent key-distribution schemes. Its quantum and classical winning probabilities are stated, but the corresponding entropy lower bounds and key rates are not derived.

The authors note that the comparison requires a separate analysis, particularly because the relevant conditional entropy and finite-round effects differ from those of the Parity Magic Square and ordinary Parity-CHSH protocols. A tight comparison would clarify which protocol is superior across noise regimes and finite- versus asymptotic-round settings.

References

We leave a tight comparison between the key rates obtained from $pMSG, pCHSH$ and the Parallel Parity-CHSH game, as an interesting open question for future work.

— Device-Independent Conference Keys from Parity-Extended Games  (2610.01025 - Chakraborty et al., 1 Oct 2026) in Appendix, Section “The Parallel Parity-CHSH game”