## Don Jean Baptiste Anoman - F. Arnault - S. Naldi

# Quantum Random Number Generator based on Violations of the Free CHSH-3
Inequality

created by naldi on 18 May 2020

[

BibTeX]

*preprint*

**Inserted:** 18 may 2020

**Last Updated:** 18 may 2020

**Year:** 2020

**Abstract:**

We describe a protocol for generating random numbers based on the existence
of quantum violations of a free Clauser-Horne-Shimony-Holt inequality, namely
CHSH-3. Our method uses semidefinite programming relaxations to compute such
violations. In a standard setting the CHSH-3 inequality involves two separated
qutrits and compatible measurement, that is, commuting with each other,
yielding the known quantum bound of $1+\sqrt{11/3} \approx 2.9149$. In our
framework, $d$-dimensional quantum systems (qudits) where $d$ is not fixed a
priori, and measurement operators possibly not compatible, are allowed. This
loss of constraints yields a higher value for the maximum expectation of the
CHSH-3 inequality. Based on such upper bound on the violation of CHSH-3, we
develop a random number generator of type prepare-and-measure, but with one
part.