One-Shot Secret Sharing with Monotone Access Structures over Classical-Quantum Broadcast Channels

TL;DR

This paper introduces a one-shot secret sharing scheme over classical-quantum broadcast channels with monotone access structures, providing achievable rates and bounds, and extending to asymptotic scenarios.

Contribution

It develops the first one-shot secret sharing rates and bounds for quantum broadcast channels with monotone access structures, including asymptotic analysis.

Findings

Achievable one-shot secret sharing rates are established.

Converse bounds are derived for arbitrary monotone access structures.

Results coincide with classical secret sharing capacity when all shares are needed.

Abstract

We consider a secret sharing setting with a monotone access structure involving a control node and $L$ users, connected via a classical-quantum broadcast channel whose input is controlled by the control node, referred to as the dealer. Unlike traditional secret sharing settings, where the dealer fully controls the shares given to each user, in our model, the dealer encodes the secret for transmission over the broadcast channel. This means that the shares received by users are perturbed by the channel and are not fully controlled by the dealer. Our main results are achievable one-shot secret sharing rates, as well as converse bounds for arbitrary monotone access structures. We further derive second-order and asymptotic achievable rates for arbitrary monotone access structures. In the special case where all shares are required to recover the secret, we show that our result coincides with the existing secret sharing capacity over classical channels.