The enhanced separability criteria based on equiangular tight frames

Abstract 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).