Genuine multiparty quantum entanglement suppresses multiport classical information transmission

We establish a universal complementarity relation between the capacity of classical information transmission by employing a multiparty quantum state as a multiport quantum channel, and the corresponding genuine multipartite entanglement. The classical information transfer is from a sender to several receivers by using the quantum dense coding protocol with the multiparty quantum state shared between the sender and several receivers. The relation is derived when the multiparty entanglement is the relative entropy of entanglement as well as when it is the generalized geometric measure. The relation holds for arbitrary pure or mixed quantum states of an arbitrary number of parties in arbitrary dimensions.