Local finite rate semi device independent randomness expansion from quantum contextuality

Abstract: Finite rate randomness expansion (RE) which is secure against quantum adversaries is a crucial information processing task which is well studied in the case of two non-communicating parties sharing Bell non-local correlations in a device independent manner. In this paper we show that contextual correlations with only a single localized party are sufficient for RE in a semi-device independent (SDI) manner. We propose a template SDI-RE protocol which is applicable for arbitrary $N$-cycle non-contextuality (NC) inequalities and derive its RE rate under finite statistics. As a special case, we also highlight the advantages of the situation when RE is constrained by Clauser-Horne-Shimony-Holt (CHSH) inequality but with characterized measurements implemented by only a single party. Our template protocol also incorporates non-ideal statistics which may not satisfy perfect commutativity and perfect repeatability, both of which are necessary in a loophole-free test of NC inequalities. As such, several recent experimental implementations of significantly loophole-free tests of NC inequalities can be modified for secure RE following our approach.