Conference Key Agreement and Quantum Sharing of Classical Secrets with Noisy GHZ States

TL;DR

This paper introduces efficient distillation schemes for multi-partite CSS-states, enabling secure conference key agreement and quantum secret sharing even with noisy GHZ states, and proposes practical prepare-and-measure protocols.

Contribution

It presents novel distillation methods for CSS-states, linking them to bipartite graph states, and develops secure cryptographic protocols that work beyond Bell inequality violations.

Findings

Protocols remain secure without Bell inequality violation.

High yield and fidelity thresholds for secure operation.

Experimental schemes involving only bipartite entanglement.

Abstract

We propose a wide class of distillation schemes for multi-partite entangled states that are CSS-states. Our proposal provides not only superior efficiency, but also new insights on the connection between CSS-states and bipartite graph states. We then consider the applications of our distillation schemes for two cryptographic tasks--namely, (a) conference key agreement and (b) quantum sharing of classical secrets. In particular, we construct ``prepare-and-measure'' protocols. Also we study the yield of those protocols and the threshold value of the fidelity above which the protocols can function securely. Surprisingly, our protocols will function securely even when the initial state does not violate the standard Bell-inequalities for GHZ states. Experimental realization involving only bi-partite entanglement is also suggested.