Robustness self-testing of states and measurements in the prepare-and-measure scenario with 3 → 1 random access code*
Shi-Hui Wei, Fen-Zhuo Guo, Xinhui Li, Qiaoyan Wen · Chinese Physics B · 2019
Recently, Tavakoli et al. proposed a self-testing scheme in the prepare-and-measure scenario, showing that self-testing is not necessarily based on entanglement and violation of a Bell inequality [Phys. Rev. A 98 062307 (2018)]. They realized the self-testing of preparations and measurements in an N → 1 ( N ≥ 2 ) random access code (RAC), and provided robustness bounds in a 2 → 1 RAC. Since all N → 1 RACs with shared randomness are combinations of 2 → 1 and 3 → 1 RACs, the 3 → 1 RAC is just as important as the 2 → 1 RAC. In this paper, we find a set of preparations and measurements in the 3 → 1 RAC, and use them to complete the robustness self-testing analysis in the prepare-and-measure scenario. The method is robust to small but inevitable experimental errors.