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)

Error exponents in quantum information theory

Alexander Semenovich Holevo

Published Nov 13, 2002• 0 citations
Publisher

Abstract

In this paper we survey results and open problems concerning error exponents and the reliability function of a quantum communication channel.
DOI
10.1109/isit.2001.936116

Related papers

Information-theoretic aspects of quantum channel discrimination

Mark M. Wilde

I will give an overview of quantum channel discrimination, reviewing the task, its operational significance, connections to other information-theoretic tasks like communication and estimation, and progress in establishing characterizations and bounds on error exponents. Inevitably, quantum effects and additivity issues arise in quantum channel discrimination, revealing fundamental differences between classical and quantum information. Delivered as a talk at "Additivity Problems in Quantum and Classical Information Theory", held at Banff International Research Station during July 12-17, 2026

•Jul 17, 2026•0 citations

Quantum channels and memory effects

Filippo Caruso, Vittorio Giovannetti, Cosmo Lupo +1 more

Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.

arXiv:1207.5435•Reviews of Modern Physics•Dec 10, 2014•329 citations

Capacity of the noisy quantum channel

Seth Lloyd

An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel using the high-probability states of quantum sources. A class of quantum error-correcting codes is presented that allows the information transmitted to attain this limit. The result is a quantum analog of Shannon's bound and code for the noisy classical channel [C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Chicago, 1948)].

arXiv:quant-ph/9604015•Physical Review A•Mar 1, 1997•779 citations

Reliability Function of Classical-Quantum Channels

Ke Li, Dong Yang

We study the reliability function of general classical-quantum channels, which describes the optimal exponent of the decay of decoding error when the communication rate is below the capacity. As the main result, we prove a lower bound, in terms of the quantum Rényi information in Petz's form, for the reliability function. This resolves Holevo's conjecture proposed in 2000, a long-standing open problem in quantum information theory. It turns out that the obtained lower bound matches the upper bound derived by Dalai in 2013, when the communication rate is above a critical value. Thus, we have determined the reliability function in this high-rate case. Our approach relies on Renes' breakthrough made in 2022, which relates classical-quantum channel coding to that of privacy amplification, as well as our new characterization of the channel Rényi information.

arXiv:2407.12403•Physical Review Letters•Jan 8, 2025•11 citations

Capacities of Quantum Channels and How to Find Them

Peter W. Shor

Abstract: We survey what is known about the information transmitting capacities of quantum channels, and give a proposal for how to calculate some of these capacities using linear programming. 1

•Jan 1, 2003•38 citations

Capacity of a memoryless quantum communication channel

T. Fujiwara, Hiroshi Nagaoka

We introduce a proper framework of coding problems for a quantum memoryless channel and derive an asymptotic formula for the channel capacity having an operational significance. Some general lower and upper bounds for the quantum channel capacity are also derived.

IEEE International Symposium on Information Theory (ISIT)•Nov 19, 2002•1 citation
I will give an overview of quantum channel discrimination, reviewing the task, its operational significance, connections to other information-theoretic tasks like communication and estimation, and progress in establishing characterizations and bounds on error exponents. Inevitably, quantum effects and additivity issues arise in quantum channel discrimination, revealing fundamental differences between classical and quantum information. Delivered as a talk at "Additivity Problems in Quantum and Classical Information Theory", held at Banff International Research Station during July 12-17, 2026
Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.
An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel using the high-probability states of quantum sources. A class of quantum error-correcting codes is presented that allows the information transmitted to attain this limit. The result is a quantum analog of Shannon's bound and code for the noisy classical channel [C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Chicago, 1948)].
We study the reliability function of general classical-quantum channels, which describes the optimal exponent of the decay of decoding error when the communication rate is below the capacity. As the main result, we prove a lower bound, in terms of the quantum Rényi information in Petz's form, for the reliability function. This resolves Holevo's conjecture proposed in 2000, a long-standing open problem in quantum information theory. It turns out that the obtained lower bound matches the upper bound derived by Dalai in 2013, when the communication rate is above a critical value. Thus, we have determined the reliability function in this high-rate case. Our approach relies on Renes' breakthrough made in 2022, which relates classical-quantum channel coding to that of privacy amplification, as well as our new characterization of the channel Rényi information.