Can bipartite classical information resources be activated?

TL;DR

This paper investigates whether non-additivity, a quantum trait, can occur in classical information theory, specifically in secret-key agreement scenarios, showing that combining certain correlations can enable secret-key distillation.

Contribution

It provides evidence that classical secret-key rates can be non-additive, revealing a new link between entanglement and classical secret-key distillation.

Findings

Correlations with bound information become secret-key distillable when combined.

Secret-key rate may be non-additive in classical information scenarios.

Highlights the subtle relation between entanglement and secret-key agreement.

Abstract

Non-additivity is one of the distinctive traits of Quantum Information Theory: the combined use of quantum objects may be more advantageous than the sum of their individual uses. Non-additivity effects have been proven, for example, for quantum channel capacities, entanglement distillation or state estimation. In this work, we consider whether non-additivity effects can be found in Classical Information Theory. We work in the secret-key agreement scenario in which two honest parties, having access to correlated classical data that are also correlated to an eavesdropper, aim at distilling a secret key. Exploiting the analogies between the entanglement and the secret-key agreement scenario, we provide some evidence that the secret-key rate may be a non-additive quantity. In particular, we show that correlations with conjectured bound information become secret-key distillable when combined. Our results constitute a new instance of the subtle relation between the entanglement and secret-key agreement scenario.