Multipartite Secret Correlations and Bound Information

TL;DR

This paper explores the extraction of secret keys among multiple parties sharing correlated information, introducing new probability distributions and revealing the existence of bound information where secret correlations cannot be distilled.

Contribution

It provides a full characterization of distillation properties for a new family of probability distributions, including examples of bound information in multipartite settings.

Findings

Identification of non-distillable secret correlations

Introduction of a new family of probability distributions

Examples of bound information in multipartite scenarios

Abstract

We consider the problem of secret key extraction when $n$ honest parties and an eavesdropper share correlated information. We present a family of probability distributions and give the full characterization of its distillation properties. This formalism allows us to design a rich variety of cryptographic scenarios. In particular, we provide examples of multipartite probability distributions containing non-distillable secret correlations, also known as bound information.