Randomness expansion secured by quantum contextuality

Abstract

The output randomness from a random number generator can be certified by observing the violation of quantum contextuality inequalities based on the Kochen-Specker theorem. Contextuality can be tested in a single quantum system, which significantly simplifies the experimental requirements to observe the violation comparing to the ones based on nonlocality tests. However, it is not yet resolved as to how to ensure compatibilities for sequential measurements that is required in contextuality tests. Here, we employ a modified Klyachko-Can-Binicioǧlu-Shumovsky contextuality inequality, which can ease the strict compatibility requirement on measurements. On a trapped single 138Ba+ ion system, we experimentally demonstrate violation of the contextuality inequality and realize quantum random number expansion by closing detection loopholes. We perform 1.29×108 trials of experiments and extract a randomness of 5.28×105 bits with a speed of 270bitss-1. Our demonstration paves the way for practical high-speed spot-checking quantum random number expansion and other secure information processing applications.