Hyperdense coding and superadditivity of classical capacities in hypersphere theories

TL;DR

This paper explores hyperdense coding in generalized probabilistic theories with hyperball state spaces, demonstrating superadditive classical capacities and protocols surpassing quantum limits, at the cost of certain physical principles.

Contribution

It introduces a class of theories with hyperball state spaces where hyperdense coding enables superadditive capacities, extending quantum superdense coding beyond traditional limits.

Findings

Hyperdense coding protocols encode more bits than quantum protocols.

Superadditivity of classical capacities is demonstrated with entangled systems.

Protocols violate tomographic locality or dynamical reversibility.

Abstract

In quantum superdense coding, two parties previously sharing entanglement can communicate a two bit message by sending a single qubit. We study this feature in the broader framework of general probabilistic theories. We consider a particular class of theories in which the local state space of the communicating parties corresponds to Euclidean 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 coding protocols such that log_2 (n+1) bits are communicated if entanglement is previously shared by the communicating parties. For n > 3, these protocols are more powerful 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 this phenomenon hyperdense coding. Our hyperdense coding protocols imply superadditive classical capacities: two entangled systems can encode log_2 (n+1) > 2 bits, even though each system individually encodes at most one bit. In our examples, hyperdense coding and superadditivity of classical capacities come at the expense of violating tomographic locality or dynamical continuous reversibility.