Quantum Coding Bounds and a Closed-Form Approximation of the Minimum Distance Versus Quantum Coding Rate
The tradeoff between the quantum coding rate and the associated error correction capability is characterized by the quantum coding bounds. The unique solution for this tradeoff does not exist, but the corresponding lower and the upper bounds can be found in the literature. In this treatise, we surve...
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doaj-b7aeafadc7d34181bc1baee1e2a01a302021-03-29T20:16:55ZengIEEEIEEE Access2169-35362017-01-015115571158110.1109/ACCESS.2017.27163677950914Quantum Coding Bounds and a Closed-Form Approximation of the Minimum Distance Versus Quantum Coding RateDaryus Chandra0https://orcid.org/0000-0003-2406-7229Zunaira Babar1Hung Viet Nguyen2Dimitrios Alanis3Panagiotis Botsinis4Soon Xin Ng5Lajos Hanzo6https://orcid.org/0000-0002-2636-5214School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.The tradeoff between the quantum coding rate and the associated error correction capability is characterized by the quantum coding bounds. The unique solution for this tradeoff does not exist, but the corresponding lower and the upper bounds can be found in the literature. In this treatise, we survey the existing quantum coding bounds and provide new insights into the classical to quantum duality for the sake of deriving new quantum coding bounds. Moreover, we propose an appealingly simple and invertible analytical approximation, which describes the tradeoff between the quantum coding rate and the minimum distance of quantum stabilizer codes. For example, for a half-rate quantum stabilizer code having a code word length of n = 128, the minimum distance is bounded by 11 <; d <; 22, while our formulation yields a minimum distance of d = 16 for the above-mentioned code. Ultimately, our contributions can be used for the characterization of quantum stabilizer codes.https://ieeexplore.ieee.org/document/7950914/Quantum error correction codesquantum stabilizer codesquantum coding bound |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Daryus Chandra Zunaira Babar Hung Viet Nguyen Dimitrios Alanis Panagiotis Botsinis Soon Xin Ng Lajos Hanzo |
spellingShingle |
Daryus Chandra Zunaira Babar Hung Viet Nguyen Dimitrios Alanis Panagiotis Botsinis Soon Xin Ng Lajos Hanzo Quantum Coding Bounds and a Closed-Form Approximation of the Minimum Distance Versus Quantum Coding Rate IEEE Access Quantum error correction codes quantum stabilizer codes quantum coding bound |
author_facet |
Daryus Chandra Zunaira Babar Hung Viet Nguyen Dimitrios Alanis Panagiotis Botsinis Soon Xin Ng Lajos Hanzo |
author_sort |
Daryus Chandra |
title |
Quantum Coding Bounds and a Closed-Form Approximation of the Minimum Distance Versus Quantum Coding Rate |
title_short |
Quantum Coding Bounds and a Closed-Form Approximation of the Minimum Distance Versus Quantum Coding Rate |
title_full |
Quantum Coding Bounds and a Closed-Form Approximation of the Minimum Distance Versus Quantum Coding Rate |
title_fullStr |
Quantum Coding Bounds and a Closed-Form Approximation of the Minimum Distance Versus Quantum Coding Rate |
title_full_unstemmed |
Quantum Coding Bounds and a Closed-Form Approximation of the Minimum Distance Versus Quantum Coding Rate |
title_sort |
quantum coding bounds and a closed-form approximation of the minimum distance versus quantum coding rate |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2017-01-01 |
description |
The tradeoff between the quantum coding rate and the associated error correction capability is characterized by the quantum coding bounds. The unique solution for this tradeoff does not exist, but the corresponding lower and the upper bounds can be found in the literature. In this treatise, we survey the existing quantum coding bounds and provide new insights into the classical to quantum duality for the sake of deriving new quantum coding bounds. Moreover, we propose an appealingly simple and invertible analytical approximation, which describes the tradeoff between the quantum coding rate and the minimum distance of quantum stabilizer codes. For example, for a half-rate quantum stabilizer code having a code word length of n = 128, the minimum distance is bounded by 11 <; d <; 22, while our formulation yields a minimum distance of d = 16 for the above-mentioned code. Ultimately, our contributions can be used for the characterization of quantum stabilizer codes. |
topic |
Quantum error correction codes quantum stabilizer codes quantum coding bound |
url |
https://ieeexplore.ieee.org/document/7950914/ |
work_keys_str_mv |
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