Separability criteria and entanglement witnesses from mutually unbiased equiangular tight frames

The detection of quantum entanglement is an essential issue in the theory of quantum information. Recently, an elegant separability criterion to detect the entanglement of arbitrary-dimensional bipartite states is presented in Shi (2024 J. Phys. A: Math. Theor. 57 075302) by applying the positive operator valued measurements based on the equiangular tight frames (ETFs). Here we derive two enhanced separability criteria for detecting bipartite entanglement in arbitrary-dimensional quantum states using ETFs. Furthermore, we prove that they are not weaker than the criterion proposed in Shi (2024 J. Phys. A: Math. Theor. 57 075302).

In quantum information theory, measurements are represented by positive, operator-valued measures. In this paper, we use the operators corresponding to generalized equiangular measurements to construct positive maps. Their positivity follows from the properties of index of coincidence for few equiangular tight frames. These maps give rise to entanglement witnesses, which include as special cases many important classes considered in the literature. Additionally, we introduce separability criteria based on the correlation matrix and analyze them for various types of measurements.