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:1903.00199 · IEEE Transactions on Information Theory

Bounding and Estimating the Classical Information Rate of Quantum Channels With Memory

Michael X. Cao, Pascal O. Vontobel

Published Mar 10, 2020• 2 citations
arXivHTMLPDF

Abstract

We consider the scenario of classical communication over a finite-dimensional quantum channel with memory using a separable-state input ensemble and local output measurements. We propose algorithms for estimating the information rate of such communication setups, along with algorithms for bounding the information rate based on so-called auxiliary channels. Some of the algorithms are extensions of their counterparts for (classical) finite-state-machine channels. Notably, we discuss suitable graphical models for doing the relevant computations. Moreover, the auxiliary channels are learned in a data-driven approach; i.e., only input/output sequences of the true channel are needed, but not the channel model of the true channel.

DOI
10.1109/tit.2020.2979840

Related papers

Estimating the information rate of a channel with classical input and output and a quantum state

Michael X. Cao, Pascal O. Vontobel

We consider the problem of transmitting classical information over a time-invariant channel with memory. A popular class of time-invariant channels with memory are finite-state-machine channels, where a classical state evolves over time and governs the relationship between the classical input and the classical output of the channel. For such channels, various techniques have been developed for estimating and bounding the information rate. In this paper we consider a class of time-invariant channels where a quantum state evolves over time and governs the relationship between the classical input and the classical output of the channel. We propose algorithms for estimating and bounding the information rate of such channels. In particular, we discuss suitable graphical models for doing the relevant computations.

arXiv:1705.01041•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2017•7 citations

Optimizing Bounds on the Classical Information Rate of Quantum Channels with Memory

Michael X. Cao, Pascal O. Vontobel

We are interested in classical communication over a quantum channel with memory, in particular, we are interested in quantum-auxiliary-channel-based upper and lower bounds on the information rate. Toward improving these bounds, we propose efficient algorithms for optimizing the auxiliary channel. From a practical perspective, the lower bounds are of significant interest because they represent mismatched information rates, i.e., information rates that are achievable by a communication system where the decoder is matched to the auxiliary channel, instead of the original channel. Moreover, the auxiliary channels are learned in a data-driven approach, i.e., only input/output sequences of the true channel are needed, but not the channel model of the true channel.

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

Variational estimation of capacity bounds for quantum channels

Junaid ur Rehman, Seongjin Hong, Yong‐Su Kim +1 more

We propose a framework to variationally obtain detectable capacity bounds for quantum channels. The proposal of this framework is motivated by the difficulty of estimating the von Neumann entropy of an unknown quantum state. Instead of estimating the von Neumann entropy at the channel output, we propose to estimate the state purity---which can be measured by a single measurement setting---followed by bounding the von Neumann entropy from above and below. This procedure leads to new upper and lower bounds on various communication rates of quantum channels for some fixed input states. Then, by utilizing the variational method to find optimal input states we obtain lower bounds on (i) the quantum capacity of arbitrary channels, (ii) the entanglement-assisted classical capacity of arbitrary channels, and (iii) the classical capacity of covariant channels. Corresponding to these lower bounds, we also obtain upper bounds on (i) $N$-shot coherent information, (ii) the entanglement-assisted classical capacity, and (iii) the $N$-shot Holevo capacity of arbitrary quantum channels. All these bounds can be estimated by a single measurement setting without needing a full process tomography or any further a priori knowledge, e.g., preferred basis of the channel.

Physical Review A•Mar 28, 2022•5 citations

Bounds on classical information capacities for a class of quantum memory channels

Garry Bowen, Igor Devetak, Stefano Mancini

The maximum rates for information transmission through noisy quantum channels has primarily been developed for memoryless channels, where the noise on each transmitted state is treated as independent. Many real-world communication channels experience noise which is modeled better by errors that are correlated between separate channel uses. In this Brief Report, upper bounds on the classical information capacities of a class of quantum memory channels are derived. The class of channels consists of indecomposable quantum memory channels, a generalization of classical indecomposable finite-state channels.

arXiv:quant-ph/0312216•Physical Review A•Mar 24, 2005•46 citations

Second order refinements for the classical capacity of quantum channels with separable input states

Marco Tomamichel, Vincent Y. F. Tan

We study the non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of information that can be transmitted when the channel is used a finite number of times and a finite average decoding error is permissible. We show that, if we restrict the encoder to use ensembles of separable states, the non-asymptotic fundamental limit admits a Gaussian approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the number of channel uses tends to infinity. To do so, several important properties of quantum information quantities, such as the capacity-achieving output state, the divergence radius, and the channel dispersion, are generalized from their classical counterparts. Further, we exploit a close relation between classical-quantum channel coding and quantum binary hypothesis testing and rely on recent progress in the non-asymptotic characterization of quantum hypothesis testing and its Gaussian approximation.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2014•0 citations

Characterising memory in quantum channel discrimination via constrained separability problems

Ties-A. Ohst, Shijun Zhang, H. Chau Nguyen +2 more

Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a known random ensemble should be determined by applying it for a single time. In this paper, we characterise the quality of channel discrimination protocols when the quantum memory, quantified by the auxiliary dimension, is limited. This is achieved by formulating the problem in terms of separable quantum states with additional affine constraints that all of their factors in each separable decomposition obey. We discuss the computation of upper and lower bounds to the solutions of such problems which allow for new insights into the role of memory in channel discrimination. In addition to the single-copy scenario, this methodological insight allows to systematically characterise quantum and classical memories in adaptive channel discrimination protocols. Especially, our methods enabled us to identify channel discrimination scenarios where classical or quantum memory is required, and to identify the hierarchical and non-hierarchical relationships within adaptive channel discrimination protocols.

arXiv:2411.08110•Quantum•Jan 28, 2026•1 citation
We consider the scenario of classical communication over a finite-dimensional quantum channel with memory using a separable-state input ensemble and local output measurements. We propose algorithms for estimating the information rate of such communication setups, along with algorithms for bounding the information rate based on so-called auxiliary channels. Some of the algorithms are extensions of their counterparts for (classical) finite-state-machine channels. Notably, we discuss suitable graphical models for doing the relevant computations. Moreover, the auxiliary channels are learned in a data-driven approach; i.e., only input/output sequences of the true channel are needed, but not the channel model of the true channel.
We consider the problem of transmitting classical information over a time-invariant channel with memory. A popular class of time-invariant channels with memory are finite-state-machine channels, where a classical state evolves over time and governs the relationship between the classical input and the classical output of the channel. For such channels, various techniques have been developed for estimating and bounding the information rate. In this paper we consider a class of time-invariant channels where a quantum state evolves over time and governs the relationship between the classical input and the classical output of the channel. We propose algorithms for estimating and bounding the information rate of such channels. In particular, we discuss suitable graphical models for doing the relevant computations.
We are interested in classical communication over a quantum channel with memory, in particular, we are interested in quantum-auxiliary-channel-based upper and lower bounds on the information rate. Toward improving these bounds, we propose efficient algorithms for optimizing the auxiliary channel. From a practical perspective, the lower bounds are of significant interest because they represent mismatched information rates, i.e., information rates that are achievable by a communication system where the decoder is matched to the auxiliary channel, instead of the original channel. Moreover, the auxiliary channels are learned in a data-driven approach, i.e., only input/output sequences of the true channel are needed, but not the channel model of the true channel.
We propose a framework to variationally obtain detectable capacity bounds for quantum channels. The proposal of this framework is motivated by the difficulty of estimating the von Neumann entropy of an unknown quantum state. Instead of estimating the von Neumann entropy at the channel output, we propose to estimate the state purity---which can be measured by a single measurement setting---followed by bounding the von Neumann entropy from above and below. This procedure leads to new upper and lower bounds on various communication rates of quantum channels for some fixed input states. Then, by utilizing the variational method to find optimal input states we obtain lower bounds on (i) the quantum capacity of arbitrary channels, (ii) the entanglement-assisted classical capacity of arbitrary channels, and (iii) the classical capacity of covariant channels. Corresponding to these lower bounds, we also obtain upper bounds on (i) NNN-shot coherent information, (ii) the entanglement-assisted classical capacity, and (iii) the NNN-shot Holevo capacity of arbitrary quantum channels. All these bounds can be estimated by a single measurement setting without needing a full process tomography or any further a priori knowledge, e.g., preferred basis of the channel.
The maximum rates for information transmission through noisy quantum channels has primarily been developed for memoryless channels, where the noise on each transmitted state is treated as independent. Many real-world communication channels experience noise which is modeled better by errors that are correlated between separate channel uses. In this Brief Report, upper bounds on the classical information capacities of a class of quantum memory channels are derived. The class of channels consists of indecomposable quantum memory channels, a generalization of classical indecomposable finite-state channels.
We study the non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of information that can be transmitted when the channel is used a finite number of times and a finite average decoding error is permissible. We show that, if we restrict the encoder to use ensembles of separable states, the non-asymptotic fundamental limit admits a Gaussian approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the number of channel uses tends to infinity. To do so, several important properties of quantum information quantities, such as the capacity-achieving output state, the divergence radius, and the channel dispersion, are generalized from their classical counterparts. Further, we exploit a close relation between classical-quantum channel coding and quantum binary hypothesis testing and rely on recent progress in the non-asymptotic characterization of quantum hypothesis testing and its Gaussian approximation.
Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a known random ensemble should be determined by applying it for a single time. In this paper, we characterise the quality of channel discrimination protocols when the quantum memory, quantified by the auxiliary dimension, is limited. This is achieved by formulating the problem in terms of separable quantum states with additional affine constraints that all of their factors in each separable decomposition obey. We discuss the computation of upper and lower bounds to the solutions of such problems which allow for new insights into the role of memory in channel discrimination. In addition to the single-copy scenario, this methodological insight allows to systematically characterise quantum and classical memories in adaptive channel discrimination protocols. Especially, our methods enabled us to identify channel discrimination scenarios where classical or quantum memory is required, and to identify the hierarchical and non-hierarchical relationships within adaptive channel discrimination protocols.