Robustness of quantum randomness expansion protocols in the presence of noise

TL;DR

This paper analyzes the robustness of quantum randomness expansion protocols under noise, showing that different Bell operators are optimal depending on noise levels and that single operators are often insufficient.

Contribution

It introduces a comparison of various Bell-type certificates for randomness generation, highlighting the importance of protocol adaptation to noise conditions.

Findings

Different Bell operators are optimal at different noise levels.

Using a single Bell operator is rarely optimal for randomness certification.

Protocols need to adapt based on the expected noise in the device.

Abstract

In this paper we investigate properties of several randomness generation protocols in the device independent framework. Using Bell-type inequalities it is possible to certify that the numbers generated by an untrusted device are indeed random. We present a selection of certificates which guarantee two bits of randomness for each run of the experiment in the noiseless case and require the parties to share a maximally entangled state. To compare them we study their efficiency in the presence of white noise. We find that for different amounts of noise different operators are optimal for certifying most randomness. Therefore the vendor of the device should use different protocols depending on the amount of noise expected to occur. Another of our results that we find particularly interesting is that using a single Bell operator as a figure of merit is rarely optimal.