Multipartite entanglement detection based on the generalized state-dependent entropic uncertainty relation for multiple measurements

We present the generalized state-dependent entropic uncertainty relations in a multiple measurements setting and the optimal lower bound is obtained by considering different measurement sequences. We then apply this uncertainty relation to witness entanglement and give the experimentally accessible lower bounds on both bipartite and tripartite entanglements. This method of detecting entanglement is applied to a physical system of two particles on a one-dimensional lattice and Greenberger-Horne-Zeilinger (GHZ)-Werner state. It is shown that, for measurements that are not in mutually unbiased bases, this generalized entropic uncertainty relation is superior to the previous state-independent one in entanglement detection. Furthermore, we conduct a demonstration of multipartite entanglement detection of GHZ states up to ten qubits on the Quafu cloud quantum computation platform. Our results might play important roles in detecting multipartite entanglement experimentally.