Mutually unbiased measurements-induced lower bounds of concurrence

We propose a family of lower bounds for concurrence in quantum systems using mutually unbiased measurements, which prove more effective in entanglement estimation compared to existing methods. Through analytical and numerical examples, we demonstrate that these bounds outperform conventional approaches, particularly in capturing finer entanglement features. Additionally, we introduce separability criterions based on MUMs for arbitrary $d$-dimensional bipartite systems, the research results show that our criterion has more advantages than the existing criteria.