Device-independent randomness certification using multiple copies of entangled states

Abstract

We demonstrate to what extent many copies of maximally entangled two-qubit states enable for generating a greater amount of certified randomness than that can be certified from a single copy. Although it appears that greater the dimension of the system implies a higher amount of randomness, the non-triviality lies in the device-independent simultaneous certification of generated randomness from many copies of entangled states. This is because, most of the two-outcome Bell inequalities (viz., Clauser-Horne-Shimony-Holt, Elegant, or Chain Bell inequality) are optimized for a single copy of two-qubit entangled state. Thus, such Bell inequalities can certify neither many copies of entangled states nor a higher amount of randomness. In this work, we suitably invoke a family of $n$-settings Bell inequalities which is optimized for $\lfloor n/2\rfloor$ copies of maximally entangled two-qubit states, thereby, possess the ability to certify more randomness from many copies of two-qubit entangled state.