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arXiv:1911.07753 · Journal of Mathematical Physics

Universal superposition codes: Capacity regions of compound quantum broadcast channel with confidential messages

Holger Boche, Gisbert Janßen, Sajad Saeedinaeeni

Published Apr 1, 2020• 13 citations
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Abstract

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.

DOI
10.1063/1.5139622

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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.
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 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.
We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel coding by using generalized packing lemmas for the type method. Using our classical-quantum universal superposition code, we establish the capacity region of a classical-quantum compound broadcast channel with degraded message sets. Our universal classical-quantum multiple access channel codes have two types of codes. One is a code with joint decoding and the other is a code with separate decoding. It is not so easy to construct a former code that universally achieves general points of the capacity region beyond corner points. First, we construct the latter code that universally achieves general points of the capacity region. Then, converting the latter code to the former coder, we construct the above desired code with the former type.
We derive universal codes for simultaneous transmission of classical messages and entanglement through quantum channels, possibly under attack of a malignant third party. These codes are robust to different kinds of channel uncertainty. We show these codes to be optimal by giving a multi-letter characterization of regions corresponding to capacity of compound quantum channels for simultaneously transmitting and generating entanglement with classical messages. Also, we give dichotomy statements in which we characterize the capacity of arbitrarily varying quantum channels for simultaneous transmission of classical messages and entanglement.
We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel code by using generalized packing lemmas for the type method. Using our classical-quantum universal superposition code, we establish the capacity region of a classical-quantum compound broadcast channel with degraded message sets. Our universal classical-quantum multiple access channel codes have two types of codes. One is a code with joint decoding and the other is a code with separate decoding. It is not so easy to construct a former code that universally achieves general points of the capacity region beyond corner points. First, we construct the latter code that universally achieves general points of the capacity region. Then, converting the latter code to the former code, we construct the above desired code with the former type. A full version of this paper is accessible at http://arxiv.org/abs/2011.00410
We derive universal codes for simultaneous transmission of classical messages and entanglement through quantum channels, possibly under the attack of a malignant third party. These codes are robust to different kinds of channel uncertainties. To construct such universal codes, we invoke and generalize the properties of random codes for classical and quantum message transmission through quantum channels. We show these codes to be optimal by giving a multi-letter characterization of regions corresponding to capacity of compound quantum channels for simultaneously transmitting and generating entanglement with classical messages. In addition, we give dichotomy statements in which we characterize the capacity of arbitrarily varying quantum channels for simultaneous transmission of classical messages and entanglement. These include cases where the malignant jammer present in the arbitrarily varying channel model is classical (chooses channel states of the product form) and fully quantum (is capable of general attacks not necessarily of the product form).
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.