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arXiv:1810.10406 · Journal of Mathematical Physics

Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks

Holger Boche, Gisbert Janßen, Sajad Saeedinaeeni

Published Feb 1, 2019• 7 citations
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Abstract

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).

DOI
10.1063/1.5078430

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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).
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 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.
In this paper, a new model for arbitrarily varying classical-quantum channels is proposed. In this model, a jammer has side information. The communication scenario in which a jammer can select only classical inputs as a jamming sequence is considered in the first part of the paper. This situation corresponds to the standard model of arbitrarily varying classical-quantum channels. Two scenarios are considered. In the first scenario, the jammer knows the channel input, while in the second scenario the jammer knows both the channel input and the message. The transmitter and receiver share a secret random key with a vanishing key rate. The capacity for both average and maximum error criteria for both scenarios is determined in this paper. A strong converse is also proved. It is shown that all these corresponding capacities are equal, which means that additionally revealing the message to the jammer does not change the capacity. The communication scenario with a fully quantum jammer is considered in the second part of the paper. A single letter characterization for the capacity with secret random key as assistance for both average and maximum error criteria is derived in the paper.
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 consider the task of entanglement assisted message transmission under presence of a compound memoryless quantum channel. In this model, the completely positive and trace preserving map governing the channel statistics is, instead of being perfectly known, only revealed as member of a certain set of channels. Therefore, coding schemes have to be used which are simultaneously reliable for each member of this set. Utilizing universal codes for classical-quantum channels, we introduce optimal universal coding schemes for entanglement assisted message transmission of compound quantum channels. The resulting coding theorem together with a corresponding converse statement leads us to a single-letter expression for the entanglement assisted message transmission capacity of compound quantum channels.
If a sender and a receiver lack precise knowledge about the communication line that connects them, designing a scheme to reliably transmit information becomes more challenging. This has been studied in classical and quantum information theory in the context of compound channel models and arbitrarily varying channel models. However, a fully quantum version of system uncertainty allows for an even more challenging coding scenario with entangled channel uses. This type of model has previously been investigated for classical and quantum capacity. Here, we address the problem of entanglement-assisted capacity in the presence of such system uncertainty. We find that, under the assumption of a finite environment dimension, it is equal to a corresponding compound capacity. Intriguingly, our results imply that in certain fully quantum arbitrarily varying channel models, the entanglement-assisted capacity can be positive while the classical capacity is equal to zero, a phenomenon that does not occur in regular single-channel coding.