Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Randomness Extraction from Bell Violation with Continuous Parametric Down-Conversion



Thomas Gerrits, Sae Woo Nam, Adriana Lita, Lijiong Shen, Jianwei Lee, Le Phuc Thinh, Jean-Daniel Bancal, Alessandro Cere


We present a violation of the CHSH inequality without the fair sampling assumption with a continuously pumped photon pairs 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. We calculate an asymptotic rate of 1300 random bits/s.
Physical Review Letters


Bell inequality, randomness generation, superconducting detectors


Gerrits, T. , Nam, S. , Lita, A. , Shen, L. , Lee, J. , Thinh, L. , Bancal, J. and Cere, A. (2018), Randomness Extraction from Bell Violation with Continuous Parametric Down-Conversion, Physical Review Letters, [online], (Accessed May 20, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created October 8, 2018, Updated October 12, 2021