# Randomness expansion secured by quantum contextuality

## TL;DR

This paper demonstrates a practical, high-speed quantum random number expansion using a single trapped ion system that violates a modified contextuality inequality, ensuring certified randomness with simplified experimental requirements.

## Contribution

It introduces a modified contextuality inequality that relaxes measurement compatibility constraints and experimentally demonstrates secure, high-speed quantum randomness expansion with a trapped ion.

## Key findings

- Violated a modified Kochen-Specker contextuality inequality.
- Generated 8.06×10^5 random bits at 270 bits/sec.
- Closed detection loopholes in the experiment.

## 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 how to ensure compatibilities for sequential measurements that is required in contextuality tests. Here, we employ a modified Klyachko-Can-Binicio\u{g}lu-Shumovsky contextuality inequality, which can ease the strict compatibility requirement on measurements. On a trapped single \Ba ion system, we experimentally demonstrate violation of the contextuality inequality and realize self-testing quantum random number expansion by closing detection loopholes. We perform $1.29 \times 10^8$ trials of experiments and extract the randomness of $8.06 \times 10^5$ bits with a speed of 270 bits s$^{-1}$. Our demonstration paves the way for the practical high-speed spot-checking quantum random number expansion and other secure information processing applications.