Local Randomness: Examples and Application

TL;DR

This paper explores local randomness in quantum nonlocal games, providing bounds for the CHSH game and demonstrating a cryptographic application, advancing practical quantum cryptography.

Contribution

It offers a near-optimal bound on local randomness for the CHSH game and proves security for a cryptographic protocol utilizing local randomness.

Findings

Established a near-optimal bound on local randomness in the CHSH game.

Proved security of a cryptographic protocol based on local randomness.

Connected nonlocal game scores with practical cryptographic applications.

Abstract

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).