Capacity Regions for Compound Quantum Broadcast Channels with Confidential Messages

Masanori Ohya, Dėnes Petz, Noboru Watanabe

Andrea Grigorescu

The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is known only that the actual channel realization belongs to a pre-specified uncertainty set of channels and that it is constant during the entire transmission. For reliable and secure communication it is necessary to operate at a rate pair within the compound BCC capacity region. Therefore, the question of whether small variations of the uncertainty set lead to large losses of the compound BCC capacity region is of interest, and this problem is studied here. In particular, it is shown that the compound BCC model is robust, i.e., the capacity region depends continuously on the uncertainty set.

Andrea Grigorescu, Holger Boche, Rafael F. Schaefer +1 more

The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is known only that the actual channel realization belongs to a pre-specified uncertainty set of channels and that it is constant during the entire transmission. For reliable and secure communication it is necessary to operate at a rate pair within the compound BCC capacity region. Therefore, the question of whether small variations of the uncertainty set lead to large losses of the compound BCC capacity region is of interest, and this problem is studied here. In particular, it is shown that the compound BCC model is robust, i.e., the capacity region depends continuously on the uncertainty set.

Fr.

Holger Boche, Gisbert Janßen, Sajad Saeedinaeeni

We derive universal codes for transmission of broadcast and confidential messages over classical-quantum–quantum and fully quantum channels. These codes are robust to channel uncertainties considered in the compound model. To construct these codes, we generalize random codes for transmission of public messages to derive a universal superposition coding for the compound quantum broadcast channel. As an application, we give a multi-letter characterization of regions corresponding to the capacity of the compound quantum broadcast channel for transmitting broadcast and confidential messages simultaneously. This is done for two types of broadcast messages, one called public and the other common.

John Watrous