Single-Serving Quantum Broadcast Channel with Common, Individualized and Confidential Messages

The two-receiver broadcast channel with primary and third party receivers is studied. The sender wishes to reliably communicate a common (or public) message to both receivers as well as individualized and confidential messages to the primary receiver only. The third party receiver must be kept completely ignorant of the confidential message but there are no secrecy requirements associated to the individualized message. A trade-off arises between the rates of the three messages: when one of the rates is high, the other rates may need to back off to guarantee the reliable transmission of all three messages. In addition, the confidentiality requirement implies availability of local randomness at the transmitter in order to implement a stochastic encoding. This article studies the trade-off between the rates of the common, individualized and confidential messages as well as that of the local randomness in the one-shot regime of a quantum broadcast channel. We provide an achievability region, by proving a conditional version of the convex-split lemma combined with the position-based decoding, as well as a (weak) converse region. We study the asymptotic behaviour of our bounds and recover several well-known asymptotic results in the literature, including simultaneous transmission of classical and quantum information.