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

• URL: http://arxiv.org/abs/2003.00124v3
• Date: Thu, 30 Jul 2020 09:40:57 GMT
• Title: Quantum Random Number Generator based on Violations of the Free CHSH-3 Inequality
• Authors: Don Jean Baptiste Anoman, Fran\c{c}ois Arnault, and Simone Naldi
• Abstract summary: 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 protocol generates a maximal entropy and its security is based, through self testing arguments, on the attainability of the maximal violation of the free CHSH-3 for quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. Our protocol generates a maximal entropy and its security is based, through self testing arguments, on the attainability of the maximal violation of the free CHSH-3 for quantum systems.

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