Multipartite Dense Coding vs. Quantum Correlation: Noise Inverts Relative Capability of Information Transfer

A highly entangled bipartite quantum state is more advantageous for the quantum dense coding protocol than states with low entanglement. Such a correspondence, however, does not exist even for pure quantum states in the multipartite domain. We establish a connection between the multiparty capacity of classical information transmission in quantum dense coding and several multipartite quantum correlation measures of the shared state, used in the dense coding protocol. In particular, we show that for the noiseless channel, if multipartite quantum correlations of an arbitrary multipartite state of arbitrary number of qubits is the same as that of the corresponding generalized Greenberger-Horne-Zeilinger state, then the multipartite dense coding capability of former is the same or better than that of the generalized Greenberger-Horne-Zeilinger state. Interestingly, in a noisy channel scenario, where we consider both uncorrelated and correlated noise models, the relative abilities of the quantum channels to transfer classical information can get inverted by administering a sufficient amount of noise. When the shared state is an arbitrary multipartite mixed state, we also establish a link between the classical capacity for the noiseless case and multipartite quantum correlation measures.