Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

Entanglement assisted classical capacity of compound quantum channels

Holger Boche, Gisbert Janßen, Stephan Kaltenstadler

Published Jul 1, 2016• 1 citation
Publisher

Abstract

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.

DOI
10.1109/isit.2016.7541585

Related papers

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

Holger Boche, Gisbert Janßen, Sajad Saeedinaeeni

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.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2019•0 citations

Classical capacities of compound quantum channels

Igor Bjelaković, Holger Boche

We determine the capacity of compound classicalquantum channels. The capacity result for compound channels demonstrates, as in the classical setting, the existence of reliable universal classical-quantum codes in scenarios where the only a priori information about the channel used for the transmission of information is that it belongs to a given set of memoryless classical-quantum channels. Our approach is based on the universal classical approximation of the quantum relative entropy which in turn relies on the universal hypothesis testing results.

IEEE Information Theory Workshop (ITW)•May 1, 2008•2 citations

Fully Quantum Arbitrarily Varying Channel Coding for Entanglement-Assisted Communication

Paula Belzig

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.

arXiv:2404.08200•IEEE International Symposium on Information Theory (ISIT)•Jul 7, 2024•1 citation

Entanglement-assisted capacities of compound quantum channels

Mario Berta, Hrant Gharibyan, Michael Walter

We study universal quantum codes for entanglement-assisted quantum communication over compound quantum channels. In this setting, sender and receiver do not know the specific channel that will be used for communication, but only know the set that the channel is selected from. We investigate different variations of the problem: uninformed users, informed receiver, informed sender, and feedback assistance. We derive single-letter formulas for all corresponding channel capacities. Our proofs are based on one-shot decoupling bounds and properties of smooth entropies.

arXiv:1603.02282•IEEE Transactions on Information Theory•Jan 1, 2017•14 citations

Classical Capacities of Compound and Averaged Quantum Channels

Igor Bjelaković, Holger Boche

We determine the capacity of compound classical-quantum channels. As a consequence, we obtain the capacity formula for the averaged classical-quantum channels. The capacity result for compound channels demonstrates, as in the classical setting, the existence of reliable universal classical-quantum codes in scenarios where the onlya prioriinformation about the channel used for the transmission of information is that it belongs to a given set of memoryless classical-quantum channels. Our approach is based on a universal classical approximation of the quantum relative entropy which in turn relies on a universal hypothesis testing result.

IEEE Transactions on Information Theory•Jun 16, 2009•54 citations

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

Holger Boche, Gisbert Janßen, Sajad Saeedinaeeni

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).

arXiv:1810.10406•Journal of Mathematical Physics•Feb 1, 2019•7 citations
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.
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 determine the capacity of compound classicalquantum channels. The capacity result for compound channels demonstrates, as in the classical setting, the existence of reliable universal classical-quantum codes in scenarios where the only a priori information about the channel used for the transmission of information is that it belongs to a given set of memoryless classical-quantum channels. Our approach is based on the universal classical approximation of the quantum relative entropy which in turn relies on the universal hypothesis testing results.
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.
We study universal quantum codes for entanglement-assisted quantum communication over compound quantum channels. In this setting, sender and receiver do not know the specific channel that will be used for communication, but only know the set that the channel is selected from. We investigate different variations of the problem: uninformed users, informed receiver, informed sender, and feedback assistance. We derive single-letter formulas for all corresponding channel capacities. Our proofs are based on one-shot decoupling bounds and properties of smooth entropies.
We determine the capacity of compound classical-quantum channels. As a consequence, we obtain the capacity formula for the averaged classical-quantum channels. The capacity result for compound channels demonstrates, as in the classical setting, the existence of reliable universal classical-quantum codes in scenarios where the onlya prioriinformation about the channel used for the transmission of information is that it belongs to a given set of memoryless classical-quantum channels. Our approach is based on a universal classical approximation of the quantum relative entropy which in turn relies on a universal hypothesis testing result.
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).