Uniform Entanglement Frames

Abstract

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.

Uncertainty under quantum measures and quantum memory

“…If the measured particle is l 1 -partite and the quantum memory is a l 2 -partite particle such that l 1 + l 2 = L, l 1 2, then there exists a state-independent majorization bound [17] …”

“…which is state-independent. For different correlations between particles, there may exist different kind of stateindependent ω called the uniform entanglement frames [17]. In fact, if the majorization bound is written as ω…”

“…By taking all permutations on the index of (50) first, and computing the maximum over all possibilities, we obtain an optimal lower bound in the presence of quantum memory. One can also use uniform entanglement frames [17] to give a degenerate uncertainty inequality in the absence of quantum memory.…”