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

arXiv:1111.3645 · IEEE Transactions on Information Theory

Classical Codes for Quantum Broadcast Channels

Ivan Savov, Mark M. Wilde

Published Oct 6, 2015• 39 citations
arXivHTMLPDF

Abstract

We present two approaches for transmitting classical information over quantum broadcast channels. The first technique is a quantum generalization of the superposition coding scheme for the classical broadcast channel. We use a quantum simultaneous nonunique decoder and obtain a proof of the rate region stated in Yard et al., IEEE Trans. Inf. Theory 57 (10), 2011. Our second result is a quantum generalization of the Marton coding scheme. The error analysis for the quantum Marton region makes use of ideas in our earlier work and an idea recently presented by Radhakrishnan et al. in arXiv:1410.3248. Both results exploit recent advances in quantum simultaneous decoding developed in the context of quantum interference channels.

DOI
10.1109/tit.2015.2485998

Related papers

Classical codes for quantum broadcast channels

Ivan Savov, Mark M. Wilde

We discuss two techniques for transmitting classical information over quantum broadcast channels. The first technique is a quantum generalization of the superposition coding scheme for the classical broadcast channel. We use a quantum simultaneous nonunique decoder and obtain a simpler proof of the rate region recently published by Yard et al. in independent work. Our second result is a quantum Marton coding scheme, which gives the best known achievable rate region for quantum broadcast channels. Both results exploit recent advances in quantum simultaneous decoding developed in the context of quantum interference channels.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2012•16 citations

An improved rate region for the classical-quantum broadcast channel

Christoph Hirche, Ciara Morgan

We present a new achievable rate region for the two-user binary-input classical-quantum broadcast channel. The result is a generalization of the classical Marton-Gelfand-Pinsker region and is provably larger than the best previously known rate region for classical-quantum broadcast channels. The proof of achievability is based on the recently introduced polar coding scheme and its generalization to quantum network information theory.

arXiv:1501.07417•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2015•13 citations

Quantum Broadcast Channels

Jon Yard, Patrick M. Hayden, Igor Devetak

We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region. We also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels. We then consider extensions of superposition coding for channels with a quantum input, where some of the messages transmitted are quantum instead of classical, in the sense that the parties establish bipartite or tripartite GHZ entanglement. We conclude by using state merging to give achievable rates for establishing bipartite entanglement between different pair of parties with the assistance of free classical communication.

arXiv:quant-ph/0603098•IEEE Transactions on Information Theory•Oct 1, 2011•116 citations

Polar codes in quantum information theory

Christoph Hirche

Polar codes are the first capacity achieving and efficiently implementable codes for classical communication. Recently they have also been generalized to communication over classical-quantum and quantum channels. In this work we present our recent results for polar coding in quantum information theory, including applications to classical-quantum multiple access channels, interference channels and compound communication settings, including the first proof of channel coding achieving the Han-Kobayashi rate region of the interference channel without the need of a simultaneous decoder. Moreover we add to the existing framework by extending polar codes to achieve the asymmetric capacity and improving the block error probability for classical-quantum channels. In addition we use polar codes to prove a new achievable rate region for the classical-quantum broadcast channel. We also discuss polar codes for quantum communication over quantum channels and state results towards codes for compound quantum channels in this setting. We conclude by stating a list of interesting open questions to invite further research on the topic.

arXiv:1501.03737•Jan 15, 2015•10 citations

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

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 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.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2020•5 citations

Universal classical-quantum multiple access channel coding

Masahito Hayashi, Ning Cai

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

IEEE International Symposium on Information Theory (ISIT)•Jul 12, 2021•3 citations
We present two approaches for transmitting classical information over quantum broadcast channels. The first technique is a quantum generalization of the superposition coding scheme for the classical broadcast channel. We use a quantum simultaneous nonunique decoder and obtain a proof of the rate region stated in Yard et al., IEEE Trans. Inf. Theory 57 (10), 2011. Our second result is a quantum generalization of the Marton coding scheme. The error analysis for the quantum Marton region makes use of ideas in our earlier work and an idea recently presented by Radhakrishnan et al. in arXiv:1410.3248. Both results exploit recent advances in quantum simultaneous decoding developed in the context of quantum interference channels.
We discuss two techniques for transmitting classical information over quantum broadcast channels. The first technique is a quantum generalization of the superposition coding scheme for the classical broadcast channel. We use a quantum simultaneous nonunique decoder and obtain a simpler proof of the rate region recently published by Yard et al. in independent work. Our second result is a quantum Marton coding scheme, which gives the best known achievable rate region for quantum broadcast channels. Both results exploit recent advances in quantum simultaneous decoding developed in the context of quantum interference channels.
We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region. We also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels. We then consider extensions of superposition coding for channels with a quantum input, where some of the messages transmitted are quantum instead of classical, in the sense that the parties establish bipartite or tripartite GHZ entanglement. We conclude by using state merging to give achievable rates for establishing bipartite entanglement between different pair of parties with the assistance of free classical communication.
Polar codes are the first capacity achieving and efficiently implementable codes for classical communication. Recently they have also been generalized to communication over classical-quantum and quantum channels. In this work we present our recent results for polar coding in quantum information theory, including applications to classical-quantum multiple access channels, interference channels and compound communication settings, including the first proof of channel coding achieving the Han-Kobayashi rate region of the interference channel without the need of a simultaneous decoder. Moreover we add to the existing framework by extending polar codes to achieve the asymmetric capacity and improving the block error probability for classical-quantum channels. In addition we use polar codes to prove a new achievable rate region for the classical-quantum broadcast channel. We also discuss polar codes for quantum communication over quantum channels and state results towards codes for compound quantum channels in this setting. We conclude by stating a list of interesting open questions to invite further research on the topic.
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 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