One-Shot Secret Sharing with Monotone Access Structures over Classical-Quantum Broadcast Channels
2026-04-02 • Information Theory
Information Theory
AI summaryⓘ
The authors study a secret sharing system where one control node (the dealer) shares a secret with multiple users through a channel that mixes classical and quantum information. Unlike usual secret sharing where the dealer directly gives out secret pieces, here the dealer sends the secret encoded over a channel that can alter the pieces users receive. They provide formulas for how much secret information can be shared reliably in one attempt and over many attempts for different ways users can combine their pieces to recover the secret. Their results match known formulas when all users are needed to recover the secret.
secret sharingmonotone access structureclassical-quantum broadcast channeldealerone-shot secret sharingachievable ratesconverse boundssecond-order ratesasymptotic rates
Authors
Truman Welling, Rémi A. Chou, Aylin Yener
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.