Device-independent randomness certification using multiple copies of entangled states

• Device-independent randomness certification through a family of Bell expressions. Using the sum-of-squares (SOS) technique optimal quantum value expression is obtained. Many copies maximally entangled states provide an advantage over single copy. We demonstrate to what extent many two-qubit enable for generating greater amount certified than that can be from Although it appears dimension system implies higher randomness, non-triviality lies in device-independent simultaneous generated states. This because, most two-outcome inequalities (viz., Clauser-Horne-Shimony-Holt, Elegant, or Chain inequality) are optimized copy state. Thus, such certify neither nor randomness. In this work, we suitably invoke n -settings which ⌊ / 2 ⌋ states, thereby, possess ability more