Construct a genuinely multipartite consensus pseudo-telepathy game

Construct a genuinely multipartite consensus pseudo-telepathy game from which a device-independent conference key can be extracted using a single measurement setting.

Background

The paper studies a natural multiparty extension of the Magic Square game in which Alice must achieve cell-wise agreement with every other party. The authors prove a monogamy obstruction: for every number of parties N≥3, this literal consensus game has quantum value strictly below one and therefore is not a pseudo-telepathy game.

The authors’ Parity-G game construction avoids this obstruction by separating nonlocality testing from key-generation measurements. They nevertheless identify the existence of a genuinely multipartite consensus pseudo-telepathy game as an unresolved problem, motivated by the possibility of obtaining device-independent conference keys without switching between test and key measurement settings.

References

We leave it as an intriguing open problem to construct a genuinely multipartite consensus pseudo-telepathy game, from which we could extract a DI conference key with a single measurement setting.

— Device-Independent Conference Keys from Parity-Extended Games  (2610.01025 - Chakraborty et al., 1 Oct 2026) in Appendix, Section “Impossibility of a Multiparty Consensus Magic Square,” Remark (following Theorem “Monogamy obstruction”)