Comparing different approaches for generating random numbers device-independently using a photon pair source

TL;DR

This paper compares two methods for device-independent random number generation using photon pair sources, highlighting that heralded single photon sources can be more efficient despite requiring higher detection efficiencies.

Contribution

It provides a detailed theoretical and numerical comparison of two Bell test implementations for device-independent randomness, emphasizing the advantages of heralded single photon sources.

Findings

Heralded single photon sources yield higher entropy per run.

The heralded approach is more efficient in random bit generation rate.

Higher detection efficiencies are needed for heralded sources, but they still outperform conventional methods.

Abstract

What is the most efficient way to generate random numbers device-independently using a photon pair source based on spontaneous parametric down conversion (SPDC)? We consider this question by comparing two implementations of a detection-loophole-free Bell test. In particular, we study in detail a scenario where a heralded single photon source (HSPS) is used to herald path-entangled states, i.e. entanglement between two spatial modes sharing a single photon and where non-locality is revealed using photon counting preceded by small displacement operations. We start by giving a theoretical description of such a measurement. We then show how to optimize the Bell-CHSH violation through a non-perturbative calculation, taking the main experimental imperfections into account. We finally bound the amount of randomness that can be extracted and compare it to the one obtained with the conventional scenario using photon pairs entangled e.g. in polarization and analyzed through photon counting. While the former requires higher overall detection efficiencies, it is far more efficient in terms of both the entropy per experimental run and the rate of random bit generation.