Performance of Dense Coding and Teleportation for Random States --Augmentation via Pre-processing

In order to understand the resourcefulness of a natural quantum system in quantum communication tasks, we study the dense coding capacity (DCC) and teleportation fidelity (TF) of Haar uniformly generated random multipartite states of various ranks. We prove that when a rank-2 two-qubit state, a Werner state, and a pure state possess the same amount of entanglement, the DCC of a rank-2 state belongs to the envelope made by pure and Werner states. In a similar way, we obtain an upper bound via the generalized Greenberger-Horne-Zeilinger state for rank-2 three-qubit states when the dense coding with two senders and a single receiver is performed and entanglement is measured in the senders:receiver bipartition. The normalized frequency distribution of DCC for randomly generated two-, three- and four-qubit density matrices with global as well as local decodings at the receivers end are reported. The estimation of mean DCC for two-qubit states is found to be in good agreement with the numerical simulations. Universally, we observe that the performance of random states for dense coding as well as teleportation decreases with the increase of the rank of states which we have shown to be surmounted by the local pre-processing operations performed on the shared states before starting the protocols, irrespective of the rank of the states. The local pre-processing employed here is based on positive operator valued measurements along with classical communication and we show that unlike dense coding with two-qubit random states, senders operations are always helpful to probabilistically enhance the capabilities of implementing dense coding as well as teleportation.