Hyperdense coding and superadditivity of classical capacities in hypersphere theories

Abstract

In quantum superdense coding, twoartiesreviously sharing entanglement can communicate a two bit message by sending a single qubit. We study this feature in the broader framework of generalrobabilistic theories. We consider aarticular class of theories in which the local state space of the communicatingarties corresponds to Euclidian hyperballs of dimension n (the case n = 3 corresponds to the Bloch ball of quantum theory). We show that a single n-ball can encode at most one bit of information, independently of n. We introduce a bipartite extension of such theories for which there exist dense codingrotocols such that bits are communicated if entanglement isreviously shared by the communicatingarties. For theserotocols are moreowerful than the quantum one, because more than two bits are communicated by transmission of a system that locally encodes at most one bit. We call thishenomenon hyperdense coding (HDC). Our HDCrotocols imply superadditive classical capacities: two entangled systems can encode bits, even though each system individually encodes at most one bit. In our examples, HDC and superadditivity of classical capacities come at the expense of violating tomographic locality or dynamical continuous reversibility.SCOPUS: ar.jinfo:eu-repo/semantics/publishe