Problem
Research questions and friction points this paper is trying to address.
secret sharing
monotone access structures
classical-quantum broadcast channels
one-shot
One-Shot Secret Sharing with Monotone Access Structures over Classical-Quantum Broadcast Channels
🤖 AI Summary
This work addresses the challenge of uncontrolled share distribution in classical-quantum broadcast channels caused by channel perturbations. It presents the first extension of one-time secret sharing to this setting, supporting arbitrary monotone access structures. By integrating information theory, quantum communication, and secret sharing frameworks—alongside tailored code design, entropy analysis, and second-order asymptotic methods—the study establishes achievable rates and a dual converse bound for this scenario. In the special case where all users jointly recover the secret, the derived rate matches the known capacity of the corresponding classical broadcast channel, thereby confirming both the validity and generality of the proposed scheme.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
one-shot secret sharing
monotone access structures
classical-quantum broadcast channel
secret sharing capacity
second-order rates
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