Distributed Quantum Dense Coding

We introduce the notion of distributed quantum dense coding, i.e., the generalization of quantum dense coding to more than one sender and more than one receiver. We show that global operations (as compared to local operations) of the senders do not increase the information transfer capacity, in the case of a single receiver. For the case of two receivers, using local operations and classical communication, a nontrivial upper bound for the capacity is derived. We propose a general classification scheme of quantum states according to their usefulness for dense coding. In the bipartite case (for any dimensions), bound entanglement is not useful for this task.

Figure 1

Classification of multipartite quantum states, according to their usefulness for dense coding with more than one receiver. S, PBE, NBE, and D stand for separable, bound entangled states with positive partial transpose, bound entangled states with nonpositive partial transpose (if existing), and distillable non-G-DC states, respectively (each with respect to the bipartite split between the senders and receivers); see text for other notations. For a single receiver in the multiparty case, and for bipartite systems, there are shells for S, PBE, NBE, D, and G-DC only. The NBE to D boundary is not convex, provided a certain NBE state exists [26], while the convexity of G-DC to LOCC-DC boundary remains an open problem. Other boundaries are convex. In particular, the convexity of the D to G-DC boundary follows from 27.