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

Quantum Lost and Found

Gregoratti, M, Reinhard F. Werner

Published Sep 3, 2002• 68 citations
OpenAlex

Abstract

We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give a conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M. Based on these criteria we give examples of noisy channels such that (1) no information can be corrected by such a scheme (2) for some basis B there is a correcting measurement M (3) for all bases B there is an M (4) there is a measurement M which allows perfect correction for all bases B. The last case is equivalent to the possibility of correcting quantum information, and turns out to be equivalent to the channel allowing a representation as a convex combination of isometric channels. Such channels are doubly stochastic but not conversely.

Related papers

Quantum lost and found

M. Gregoratti, R. F. Werner

We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M. Based on these criteria we give examples of noisy channels such that (1) no information can be corrected by such a scheme, (2) for some basis B there is a correcting measurement M, (3) for all bases B there is an M and (4) there is a measurement M which allows perfect correction for all bases B. The last case is equivalent to the possibility of correcting quantum information, and turns out to be equivalent to the channel allowing a representation as a convex combination of isometric channels. Such channels are doubly stochastic but not conversely.

arXiv:quant-ph/0209025•Journal of Modern Optics•Apr 1, 2003•109 citations

Quantum lost and found

M. Gregoratti, Reinhard F. Werner

We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M. Based on these criteria we give examples of noisy channels such that (1) no information can be corrected by such a scheme, (2) for some basis B there is a correcting measurement M, (3) for all bases B there is an M and (4) there is a measurement M which allows perfect correction for all bases B. The last case is equivalent to the possibility of correcting quantum information, and turns out to be equivalent to the channel allowing a representation as a convex combination of isometric channels. Such channels are doubly stochastic but not conversely.

Journal of Modern Optics•Jan 1, 2003•17 citations

On quantum error-correction by classical feedback in discrete time

Gregoratti, M, Werner, R F

We consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian evolutions, in the case of fixed measurement on the environment, we give criteria for quantum information to be perfectly corrigible and characterize the related feedback. Then we analyze the case when perfect correction is not possible and, in the qubit case, we find optimal feedback maximizing the channel fidelity.

•Jan 1, 2004•28 citations

On quantum error-correction by classical feedback in discrete time

M. Gregoratti, R. F. Werner

We consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian evolutions, in the case of fixed measurement on the environment, we give criteria for quantum information to be perfectly corrigible and characterize the related feedback. Then we analyze the case when perfect correction is not possible and, in the qubit case, we find optimal feedback maximizing the channel fidelity.

arXiv:quant-ph/0403092•Journal of Mathematical Physics•May 27, 2004•38 citations

How to Correct Small Quantum Errors

M. Keyl, R. F. Werner

The theory of quantum error correction is a cornerstone of quantum information processing. It shows that quantum data can be protected against decoherence effects, which otherwise would render many of the new quantum applications practically impossible. In this paper we give a self contained introduction to this theory and to the closely related concept of quantum channel capacities. We show, in particular, that it is possible (using appropriate error correcting schemes) to send a nonvanishing amount of quantum data undisturbed (in a certain asymptotic sense) through a noisy quantum channel T, provided the errors produced by T are small enough. This text is part of a volume entitled: “Coherent evolution in noisy environments” to be published in Lecture notes in physics, Springer Verlag, http://link.springer.de/series/lnpp/, Copyright: Springer Verlag,

•Jan 1, 2002•9 citations

General bound on the accessible information for quantum channels with noisy measurements

Kurt A. Jacobs

Quantum systems may be used to transmit classical information. To do this the sender encodes information by preparing the system in one of an alphabet of possible states, and sends it to the receiver. The receiver then performs a measurement on the system in order to obtain information about which state was sent. Here we describe a general bound on the information which is accessible to the receiver in such a channel when the receivers measurement is noisy. In addition to extracting classical information, measurements also reduce the entropy of a quantum system. This is important, for example, in quantum feedback control. We discuss two corollaries of the information bound that involve this entropy reduction.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 23, 2005•0 citations
We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give a conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M. Based on these criteria we give examples of noisy channels such that (1) no information can be corrected by such a scheme (2) for some basis B there is a correcting measurement M (3) for all bases B there is an M (4) there is a measurement M which allows perfect correction for all bases B. The last case is equivalent to the possibility of correcting quantum information, and turns out to be equivalent to the channel allowing a representation as a convex combination of isometric channels. Such channels are doubly stochastic but not conversely.
We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M. Based on these criteria we give examples of noisy channels such that (1) no information can be corrected by such a scheme, (2) for some basis B there is a correcting measurement M, (3) for all bases B there is an M and (4) there is a measurement M which allows perfect correction for all bases B. The last case is equivalent to the possibility of correcting quantum information, and turns out to be equivalent to the channel allowing a representation as a convex combination of isometric channels. Such channels are doubly stochastic but not conversely.
We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M. Based on these criteria we give examples of noisy channels such that (1) no information can be corrected by such a scheme, (2) for some basis B there is a correcting measurement M, (3) for all bases B there is an M and (4) there is a measurement M which allows perfect correction for all bases B. The last case is equivalent to the possibility of correcting quantum information, and turns out to be equivalent to the channel allowing a representation as a convex combination of isometric channels. Such channels are doubly stochastic but not conversely.
We consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian evolutions, in the case of fixed measurement on the environment, we give criteria for quantum information to be perfectly corrigible and characterize the related feedback. Then we analyze the case when perfect correction is not possible and, in the qubit case, we find optimal feedback maximizing the channel fidelity.
We consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian evolutions, in the case of fixed measurement on the environment, we give criteria for quantum information to be perfectly corrigible and characterize the related feedback. Then we analyze the case when perfect correction is not possible and, in the qubit case, we find optimal feedback maximizing the channel fidelity.
The theory of quantum error correction is a cornerstone of quantum information processing. It shows that quantum data can be protected against decoherence effects, which otherwise would render many of the new quantum applications practically impossible. In this paper we give a self contained introduction to this theory and to the closely related concept of quantum channel capacities. We show, in particular, that it is possible (using appropriate error correcting schemes) to send a nonvanishing amount of quantum data undisturbed (in a certain asymptotic sense) through a noisy quantum channel T, provided the errors produced by T are small enough. This text is part of a volume entitled: “Coherent evolution in noisy environments” to be published in Lecture notes in physics, Springer Verlag, http://link.springer.de/series/lnpp/, Copyright: Springer Verlag,
Quantum systems may be used to transmit classical information. To do this the sender encodes information by preparing the system in one of an alphabet of possible states, and sends it to the receiver. The receiver then performs a measurement on the system in order to obtain information about which state was sent. Here we describe a general bound on the information which is accessible to the receiver in such a channel when the receivers measurement is noisy. In addition to extracting classical information, measurements also reduce the entropy of a quantum system. This is important, for example, in quantum feedback control. We discuss two corollaries of the information bound that involve this entropy reduction.