Qubit measurements for testing contextuality through the violation of Liang-Spekkens-Wiseman-Yu-Oh inequality

Abstract

Abstract Contextuality is a striking feature of our nature predicted by quantum theory and tested by various experiments. In a qubit system, testing contextuality requires scenarios distinct from traditional ones for systems with dimension of three or greater. In this paper, we consider the noncontextuality inequality developed by Liang-Spekkens-Wiseman and Yu-Oh, and investigate the set of three qubit measurements that can be used to test and violate this inequality. Our numerical results show that two of the three measurements can be almost arbitrary. Moreover, we have singled out several extremely interesting sets of measurements, e.g. one measurements can be white noise while the other two are arbitrarily close to white noise. These sets fulfill our knowledge about contextuality in this minimum quantum system.