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Uniform Entanglement Frames

We present several criteria for genuine multipartite entanglement from universal uncertainty relations based on majorization theory. Under non-negative Schur-concave functions, the vector-type uncertainty relation generates a family of infinitely many detectors to check genuine multipartite entanglement. We also introduce the concept of $k$-separable circles via geometric distance for probability vectors, which include at most $(k-1)$-separable states. The entanglement witness is also generalized to a universal entanglement witness which is able to detect the $k$-separable states more accurately.