Self-testing criteria for preparing-measuring qubit system

Self-testing is the high-level security verification of a claimed quantum device, confirming states prepared in device and measurements performed based solely on observed statistics. The statistical correlations can realize self-testing system preparing-and-measuring scenario. However, most previous studies focused shared entangled between devices, at present only few researches are presented existing work simultaneously self-test when some witness inequalities reach maximum violation. We focus four-state preparation selected scenarios two measurements. In this scenario, Armin Tavakoli et al. [Tavakoli A, Kaniewski J, Vértesi T, Rosset D, Brunner N 2018 <i>Phys. Rev. A</i> <b>98</b> 062307] have put forward criterion dimensional violation inequality which achieve BB84 particles corresponding Pauli addition to inequality, any statistics with deviation from cannot be self-tested. Besides, particle self-tested that criterion, resulting large number measurement systems Therefore, work, dimension we directly full further propose new criteria for qubit preparing-and-measiuring scenarios. And proven an ideal case. construct local isometry by using constructions commonly used device-independent cases, exchange target additional system, more state sets than particles. This meets requirements practical experiments various tasks different sets. addition, perform robust analysis proposed use fidelity describe closeness auxiliary system. Finally, improved dimensional-dependent NPA method optimize lower bound robustness, making under experimental noise. YALIMP software package MATLAB solver SEDUMI solve optimization problem. research increases diversity preparations beneficial actual non-entangled single systems.