Exponential quantum randomness expansion with trapped ions based on contextuality*

We report a self-testing quantum random number generator (QRNG) achieving an exponential gain of randomness expansion. Similar to Bell's theorem [1], violation of Kochen and Specker theory, which also presents the intrinsic randomness of quantum mechanics and excludes noncontextual hidden variable models, is also used to certify generated randomness [2]. Here, we employ an extended Klyachko-Can-Binicoglu-Shumovsky (KCBS) inquality [4,5] on a qutrit system of a trapped 138Ba$+$ ion system. Furthermore, by applying a spot-checking protocol of [3], our self-testing QRNG realizes exponential randomness expansion without independent and identically distributed assumption considering the most general quantum adversary scenario. The system demonstrates 1.24×10\textasciicircum 8 trials and results in randomness extraction of 2.3×10\textasciicircum 5 bits realizing a 6.6×10\textasciicircum 4 bits exponential randomness expansion with the speed of 270 bits/s. [1] S. Pironio, et al., Nature 464, 1021 (2010). [2] Mark Um, et al., Sci. Rep. 3, 1627 (2013). [3] Carl Miller and Yaoyun Shi, Siam J. Comput. 46, 1304 (2017). [4] O. Guhne, et al., Phys. Rev. A 81, 022121 (2010). [5] J. Szangolies, et al., Phys. Rev. A. 87, 050101 (2013).