Certified randomness between mistrustful players
  It is known that if two players achieve a superclassical score at a nonlocal game $G$, then their outputs are certifiably random - that is, regardless of the strategy used by the players, a third party will not be able to perfectly predict their outputs (even if he were given their inputs). We prove that for any complete-support game $G$, there is an explicit nonzero function $F_G$ such that if Alice and Bob achieve a superclassical score of $s$ at $G$, then Bob has a probability of at most $1 - F_G ( s )$ of correctly guessing Alice's output after the game is played. Our result implies that certifying global randomness through such games must necessarily introduce local randomness. 
Carl A. Miller and Yaoyun Shi
quant-ph