Entanglement detection via some classes of measurements

Abstract: Based on the mutually unbiased bases, the mutually unbiased measurements and the general symmetric informationally complete positive-operator-valued measures, we propose three separability criteria for $d$-dimensional bipartite quantum systems, which are more powerful than the corresponding ones introduced in [C. Spengler, M. Huber, S. Brierley, T. Adaktylos, and B.C. Hiesmayr, Phys. Rev. A \textbf{86}, 022311 (2012); B. Chen, T. Ma, and S.M. Fei, Phys. Rev. A \textbf{89}, 064302 (2014); B. Chen, T. Li, and S.M. Fei, arXiv:1406.7820v1 quant-ph]. Some states such as Werner states and Bell-diagonal states are used to further illustrate the efficiency of the presented criteria.