Local Randomness: Examples and Application

When two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed (C. Miller, Y. Shi, Quant. Inf. & Comp. 17, pp. 0595-0610, 2017) that such scores also imply the existence of local randomness -- that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering a near-optimal bound on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).