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:2103.02082 · IEEE International Symposium on Information Theory (ISIT)

Computing Sum of Sources over a Classical-Quantum MAC

Touheed Anwar Atif, Arun Padakandla, S. Sandeep Pradhan

Published Jul 12, 2021• 5 citations
arXivHTMLPDF

Abstract

We consider the problem of communicating a general bivariate function of two classical sources observed at the encoders of a classical-quantum multiple access channel. Building on the techniques developed for the case of a classical channel, we propose and analyze a coding scheme based on coset codes. The proposed technique enables the decoder recover the desired function without recovering the sources themselves. We derive a new set of sufficient conditions that are weaker than the current known for identified examples. This work is based on a new ensemble of coset codes that are proven to achieve the capacity of a classical-quantum point-to-point channel.

DOI
10.1109/isit45174.2021.9518261

Related papers

Computing Sum of Sources Over a Classical-Quantum MAC

Mohammad Aamir Sohail, Touheed Anwar Atif, Arun Padakandla +1 more

We consider the task of communicating a generic bivariate function of two classical correlated sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. We first propose a coding scheme based on asymptotically good algebraic structured codes, in particular, nested coset codes, and provide a set of sufficient conditions for the reconstruction of the function of the sources over a CQ-MAC. The proposed technique enables the decoder to recover the desired function without recovering the sources themselves. We further improve this by employing a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes. This coding scheme allows exploiting the symmetric structure common amongst the sources and also leverage the asymmetries. We derive a new set of sufficient conditions that strictly enlarges the largest known set of sources whose function can be reconstructed over any given CQ-MAC, and identify examples demonstrating the same. We provide these conditions in terms of single-letter quantum information-theoretic quantities.

IEEE Transactions on Information Theory•Jul 21, 2022•9 citations

Unified approach for computing sum of sources over CQ-MAC

Mohammad Aamir Sohail, Touheed Anwar Atif, S. Sandeep Pradhan

We consider the task of communicating a generic bivariate function of two classical sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. Inspired by the techniques developed for the classical setting, and employing the technique of simultaneous (joint) decoding developed for the CQ setup, we propose and analyze a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes, and the idea of embedding functions on a prime field. We derive a new set of sufficient conditions that strictly enlarge the largest known set of sources (capable of communicating the bivariate function) for any given CQ-MAC. We provide these conditions in terms of single-letter quantum information-theoretic quantities.

arXiv:2202.10403•IEEE International Symposium on Information Theory (ISIT)•Jun 26, 2022•9 citations

Communicating Over a Classical-Quantum MAC With State Information Distributed at the Senders

Arun Padakandla

We consider the problem of communicating over a classical-quantum (CQ) multiple access channel with classical state information non-causally available at the transmitters, henceforth referred to as a QMSTx. We undertake a Shannon-theoretic study and focus on the problem of characterizing inner bounds to the capacity region of a QMSTx. We propose a new coding scheme based on union coset codes - codes possessing algebraic closure properties and derive a new inner bound that subsumes the largest known inner bound based on IID random coding. We identify examples for which the derived inner bound is strictly larger.

IEEE International Symposium on Information Theory (ISIT)•Jun 26, 2022•3 citations

Communicating over a Classical-Quantum MAC with State Information Distributed at Senders

Arun Padakandla

We consider the problem of communicating over a classical-quantum (CQ) multiple access channel with random classical states non-causally available at the transmitter, referred to as a QMSTx. QMSTx is a classical-quantum multiple access analogue of the channel considered by Gelfand and Pinsker in 1980. We undertake a Shannon-theoretic study and focus on the problem of characterizing inner bounds to the capacity region of a QMSTx. We propose a new coding scheme based on \textit{union coset codes} - codes possessing algebraic properties and derive a new inner bound that subsumes the inner based on IID random coding. We identify examples for which the derived inner bound is strictly larger.

arXiv:2203.01308•Mar 2, 2022•0 citations

Simultaneous Decoding of Classical Coset Codes over 3–User Quantum Interference Channel : New Achievable Rate Regions

Fatma Gouiaa, Arun Padakandla

We undertake a Shannon theoretic study of the problem of communicating bit streams over a 3-user classical-quantum interference channel (3-CQIC) and focus on characterizing inner bounds. We design a new coding strategy based on (i) coset codes possessing algebraic closure properties and (ii) decoding POVMs to decode bi-variate interference efficiently. Needing to perform simultaneous decoding, we enhance Sen's powerful technique of tilting, smoothing, and augmentation - originally designed only for IID codes - to decode into `functions of codebooks'. Developing analysis techniques to combine all of these elements, we derive a new inner bound to the capacity region of a 3-CQIC. The derived inner bound subsumes all currently known inner bounds and is analytically proven to be strictly larger for identified examples, including non-commutative `additive' and `non-additive' ones.

arXiv:2503.07804•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2026•0 citations

The Capacity of Classical Summation over a Quantum MAC with Arbitrarily Replicated Inputs

Yuhang Yao, Syed A. Jafar

The problem of entanglement-assisted summation over a quantum multiple access channel ($\Sigma$-QMAC) is intro-duced, involving$S$servers,$K$classical$(\mathbb{F}_{d})$data streams that are replicated arbitrarily across various subsets of servers, and a receiver who wishes to compute the sum of the$K$data streams. Independent of the data, entangled quantum systems$\mathcal{Q}_{1}, \mathcal{Q}_{2}, \cdots, \mathcal{Q}_{S}$are prepared in advance and distributed to the corresponding servers. Each server$s, s\in[S]$locally manipulates its quantum system$\mathcal{Q}_{s}$according to its classical data and sends$\mathcal{Q}_{s}$to the receiver. The total communication cost is$\log_{d}\vert \mathcal{Q}_{1}\vert +\log_{d}\vert \mathcal{Q}_{2}\vert +\cdots+\log_{d}\vert \mathcal{Q}_{S}\vert$qudits, where$\vert \mathcal{Q}_{s}$denotes the dimension of$\mathcal{Q}_{s}$. Based on a measurement of the composite system$\mathcal{Q}_{1}\mathcal{Q}_{2}\cdots \mathcal{Q}_{S}$, the receiver must recover the desired sum. The rate thus achieved is defined as the number of dits$(\mathbf{F}_{d}$symbols) of the desired sum computed by the receiver per qudit (d-dimsional quantum system) of download. The capacity$C$is the supremum of the set of all achievable rates. As the main result of this work, the precise capacity of$\Sigma$-QMAC is obtained, from which it follows that quantum entanglements allow a factor of 2 gain in capacity (superdense coding gain) relative to capacity with no entanglements, in all cases (any$S, K, \mathbf{F}_{d}$and any data replication pattern) provided that the entanglement-assisted capacity does not exceed 1 dit/qudit (Holevo bound). Coding schemes based on a recent$N$-sum box abstraction are sufficient to achieve capacity.

Globecom•Dec 4, 2023•5 citations
We consider the problem of communicating a general bivariate function of two classical sources observed at the encoders of a classical-quantum multiple access channel. Building on the techniques developed for the case of a classical channel, we propose and analyze a coding scheme based on coset codes. The proposed technique enables the decoder recover the desired function without recovering the sources themselves. We derive a new set of sufficient conditions that are weaker than the current known for identified examples. This work is based on a new ensemble of coset codes that are proven to achieve the capacity of a classical-quantum point-to-point channel.
We consider the task of communicating a generic bivariate function of two classical correlated sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. We first propose a coding scheme based on asymptotically good algebraic structured codes, in particular, nested coset codes, and provide a set of sufficient conditions for the reconstruction of the function of the sources over a CQ-MAC. The proposed technique enables the decoder to recover the desired function without recovering the sources themselves. We further improve this by employing a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes. This coding scheme allows exploiting the symmetric structure common amongst the sources and also leverage the asymmetries. We derive a new set of sufficient conditions that strictly enlarges the largest known set of sources whose function can be reconstructed over any given CQ-MAC, and identify examples demonstrating the same. We provide these conditions in terms of single-letter quantum information-theoretic quantities.
We consider the task of communicating a generic bivariate function of two classical sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. Inspired by the techniques developed for the classical setting, and employing the technique of simultaneous (joint) decoding developed for the CQ setup, we propose and analyze a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes, and the idea of embedding functions on a prime field. We derive a new set of sufficient conditions that strictly enlarge the largest known set of sources (capable of communicating the bivariate function) for any given CQ-MAC. We provide these conditions in terms of single-letter quantum information-theoretic quantities.
We consider the problem of communicating over a classical-quantum (CQ) multiple access channel with classical state information non-causally available at the transmitters, henceforth referred to as a QMSTx. We undertake a Shannon-theoretic study and focus on the problem of characterizing inner bounds to the capacity region of a QMSTx. We propose a new coding scheme based on union coset codes - codes possessing algebraic closure properties and derive a new inner bound that subsumes the largest known inner bound based on IID random coding. We identify examples for which the derived inner bound is strictly larger.
We consider the problem of communicating over a classical-quantum (CQ) multiple access channel with random classical states non-causally available at the transmitter, referred to as a QMSTx. QMSTx is a classical-quantum multiple access analogue of the channel considered by Gelfand and Pinsker in 1980. We undertake a Shannon-theoretic study and focus on the problem of characterizing inner bounds to the capacity region of a QMSTx. We propose a new coding scheme based on \textit{union coset codes} - codes possessing algebraic properties and derive a new inner bound that subsumes the inner based on IID random coding. We identify examples for which the derived inner bound is strictly larger.
We undertake a Shannon theoretic study of the problem of communicating bit streams over a 3-user classical-quantum interference channel (3-CQIC) and focus on characterizing inner bounds. We design a new coding strategy based on (i) coset codes possessing algebraic closure properties and (ii) decoding POVMs to decode bi-variate interference efficiently. Needing to perform simultaneous decoding, we enhance Sen's powerful technique of tilting, smoothing, and augmentation - originally designed only for IID codes - to decode into `functions of codebooks'. Developing analysis techniques to combine all of these elements, we derive a new inner bound to the capacity region of a 3-CQIC. The derived inner bound subsumes all currently known inner bounds and is analytically proven to be strictly larger for identified examples, including non-commutative `additive' and `non-additive' ones.
The problem of entanglement-assisted summation over a quantum multiple access channel (Σ\SigmaΣ-QMAC) is intro-duced, involvingSSSservers,KKKclassical(Fd)(\mathbb{F}_{d})(Fd​)data streams that are replicated arbitrarily across various subsets of servers, and a receiver who wishes to compute the sum of theKKKdata streams. Independent of the data, entangled quantum systemsQ1,Q2,⋯ ,QS\mathcal{Q}_{1}, \mathcal{Q}_{2}, \cdots, \mathcal{Q}_{S}Q1​,Q2​,⋯,QS​are prepared in advance and distributed to the corresponding servers. Each servers,s∈[S]s, s\in[S]s,s∈[S]locally manipulates its quantum systemQs\mathcal{Q}_{s}Qs​according to its classical data and sendsQs\mathcal{Q}_{s}Qs​to the receiver. The total communication cost islog⁡d∣Q1∣+log⁡d∣Q2∣+⋯+log⁡d∣QS∣\log_{d}\vert \mathcal{Q}_{1}\vert +\log_{d}\vert \mathcal{Q}_{2}\vert +\cdots+\log_{d}\vert \mathcal{Q}_{S}\vertlogd​∣Q1​∣+logd​∣Q2​∣+⋯+logd​∣QS​∣qudits, where∣Qs\vert \mathcal{Q}_{s}∣Qs​denotes the dimension ofQs\mathcal{Q}_{s}Qs​. Based on a measurement of the composite systemQ1Q2⋯QS\mathcal{Q}_{1}\mathcal{Q}_{2}\cdots \mathcal{Q}_{S}Q1​Q2​⋯QS​, the receiver must recover the desired sum. The rate thus achieved is defined as the number of dits(Fd(\mathbf{F}_{d}(Fd​symbols) of the desired sum computed by the receiver per qudit (d-dimsional quantum system) of download. The capacityCCCis the supremum of the set of all achievable rates. As the main result of this work, the precise capacity ofΣ\SigmaΣ-QMAC is obtained, from which it follows that quantum entanglements allow a factor of 2 gain in capacity (superdense coding gain) relative to capacity with no entanglements, in all cases (anyS,K,FdS, K, \mathbf{F}_{d}S,K,Fd​and any data replication pattern) provided that the entanglement-assisted capacity does not exceed 1 dit/qudit (Holevo bound). Coding schemes based on a recentNNN-sum box abstraction are sufficient to achieve capacity.