# Publicness, Privacy and Confidentiality in the Single-Serving Quantum Broadcast Channel

## TL;DR

This paper investigates the trade-offs in transmitting public, private, and confidential messages over a quantum broadcast channel, providing one-shot achievability and converse bounds, and connecting to known asymptotic results.

## Contribution

It introduces a one-shot quantum broadcast channel model with mixed message types and derives new achievability and converse bounds using advanced quantum information techniques.

## Key findings

- Achievability and converse regions for one-shot quantum broadcast channel.
- Use of conditional convex-split lemma and position-based decoding.
- Recovery of classical asymptotic results from the quantum bounds.

## Abstract

The 2-receiver broadcast channel is studied: a network with three parties where the transmitter and one of the receivers are the primarily involved parties and the other receiver considered as third party. The messages that are determined to be communicated are classified into public, private and confidential based on the information they convey. The public message contains information intended for both parties and is required to be decoded correctly by both of them, the private message is intended for the primary party only, however, there is no secrecy requirement imposed upon it meaning that it can possibly be exposed to the third party and finally the confidential message containing information intended exclusively for the primary party such that this information must be kept completely secret from the other receiver. A trade-off arises between the rates of the three messages, when one of the rates is high, the other rates may need to be reduced to guarantee the reliable transmission of all three messages. The encoder performs the necessary equivocation by virtue of dummy random numbers whose rate is assumed to be limited and should be considered in the trade-off as well. We study this trade-off in the one-shot regime of a quantum broadcast channel by providing achievability and (weak) converse regions. In the achievability, we prove and use a conditional version of the convex-split lemma as well as position-based decoding. By studying the asymptotic behaviour of our bounds, we will recover several well-known asymptotic results in the literature.