Randomness in nonlocal games between mistrustful players

TL;DR

This paper proves that in complete-support nonlocal games, achieving a superclassical score guarantees some local randomness for each player, which is crucial for cryptography between mistrustful parties.

Contribution

It demonstrates that quantum strategies in complete-support nonlocal games inherently produce local randomness, unlike non-signaling strategies that can lack local randomness.

Findings

Superclassical score implies local randomness for each player

Quantum strategies guarantee local randomness in complete-support games

Non-signaling strategies can produce global but not local randomness

Abstract

If two quantum players at a nonlocal game G achieve a superclassical score, then their measurement outcomes must be at least partially random from the perspective of any third player. This is the basis for device-independent quantum cryptography. In this paper we address a related question: does a superclassical score at G guarantee that one player has created randomness from the perspective of the other player? We show that for complete-support games, the answer is yes: even if the second player is given the first player's input at the conclusion of the game, he cannot perfectly recover her output. Thus some amount of local randomness (i.e., randomness possessed by only one player) is always obtained when randomness is certified from nonlocal games with quantum strategies. This is in contrast to non-signaling game strategies, which may produce global randomness without any local randomness. We discuss potential implications for cryptographic protocols between mistrustful parties.