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The 2-receiver broadcast channel is studied: a network with three partieswhere the transmitter and one of the receivers are the primarily involvedparties and the other receiver considered as third party. The messages that aredetermined to be communicated are classified into public, private andconfidential based on the information they convey. The public message containsinformation intended for both parties and is required to be decoded correctlyby 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 canpossibly be exposed to the third party and finally the confidential messagecontaining information intended exclusively for the primary party such thatthis information must be kept completely secret from the other receiver. Atrade-off arises between the rates of the three messages, when one of the ratesis high, the other rates may need to be reduced to guarantee the reliabletransmission of all three messages. The encoder performs the necessaryequivocation by virtue of dummy random numbers whose rate is assumed to belimited and should be considered in the trade-off as well. We study thistrade-off in the one-shot regime of a quantum broadcast channel by providingachievability and (weak) converse regions. In the achievability, we prove anduse a conditional version of the convex-split lemma as well as position-baseddecoding. By studying the asymptotic behaviour of our bounds, we will recoverseveral well-known asymptotic results in the literature.

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