Device-independent randomness certification using multiple copies of entangled states

TL;DR

This paper explores how multiple copies of maximally entangled two-qubit states can be used to certify more randomness in a device-independent manner by employing specialized Bell inequalities optimized for multiple copies.

Contribution

It introduces a family of n-settings Bell inequalities optimized for multiple copies, enabling higher randomness certification from entangled states.

Findings

Multiple copies enable greater certified randomness.

Specialized Bell inequalities are effective for multiple copies.

Higher randomness is achievable with optimized inequalities.

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.