Device-Independent Conference Keys from Parity-Extended Games

Abstract: Device-independent conference key agreement (DI-CKA) lets a group of parties establish a shared secret key from untrusted quantum devices, with security certified by non-locality. Existing DI-CKA protocols are each built around a single Bell inequality, typically a multiparty variant of the CHSH game. DI-QKD protocols, in contrast, have been built from a much richer landscape of non-local games, and it has remained unclear how to carry this landscape over to the conference setting. We introduce $\textit{Parity-$G$ games}$, which extend any two-player game $G$ to $N$ players, for every $N$, provided $G$ has an optimal strategy in which one player measures Pauli observables. The extension preserves the quantum and classical values of $G$, and the security of the resulting $N$-party protocol follows from an analysis of the two-player game alone. Our framework recovers the Parity-CHSH game of Ribeiro, Murta and Wehner (Phys. Rev. A, 2018) as a special case. Applied to the Mermin--Peres Magic Square Game, it yields a new $N$-player pseudo-telepathy game, the $\textit{Parity Magic Square Game}$, which ideal devices win in every round. We use it to construct the $\textit{first}$ DI-CKA protocol based on a pseudo-telepathy game. We prove the protocol secure against coherent attacks. It produces up to two key bits per round, and at low noise its key rate exceeds that of the DI-CKA protocol based on the Parity-CHSH game.