Randomness extraction from Bell violation with continuous parametric down conversion

TL;DR

This paper demonstrates a loophole-free Bell test using continuous parametric down conversion and superconducting detectors, achieving high violation of Bell inequality and generating a significant rate of certified private randomness.

Contribution

It introduces a method to violate Bell inequality without fair sampling assumption using continuous photon sources and high-efficiency detectors, enabling high-rate randomness generation.

Findings

Maximum Bell violation of S=2.01602(32) achieved.

Asymptotic randomness rate of ~1300 bits/sec calculated.

Generated 617,920 random bits in 43 minutes.

Abstract

We present a violation of the CHSH inequality without the fair sampling assumption with a continuously pumped photon pair source combined with two high efficiency superconducting detectors. Due to the continuous nature of the source, the choice of the duration of each measurement round effectively controls the average number of photon pairs participating in the Bell test. We observe a maximum violation of S= 2.01602(32) with average number of pairs per round of ~0.32, compatible with our system overall detection efficiencies. Systems that violate a Bell inequality are guaranteed to generate private randomness, with the randomness extraction rate depending on the observed violation and on the repetition rate of the Bell test. For our realization, the optimal rate of randomness generation is a compromise between the observed violation and the duration of each measurement round, with the latter realistically limited by the detection time jitter. Using an extractor composably secure against quantum adversary with quantum side information, we calculate an asymptotic rate of ~1300 random bits/s. With an experimental run of 43 minutes, we generated 617,920 random bits, corresponding to ~240 random bits/s.