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Quantum coding bounds and a closed-form approximation of the minimum distance versus quantum coding rate

Quantum coding bounds and a closed-form approximation of the minimum distance versus quantum coding rate
Quantum coding bounds and a closed-form approximation of the minimum distance versus quantum coding rate
The trade-off between the quantum coding rate and the associated error correction capability is characterized by the quantum coding bounds. The unique solution for this trade-off 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 trade-off between the quantum coding rate and the minimum distance of quantum stabilizer codes. For example, for a half-rate quantum stabilizer code having a codeword 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.
11557-11581
Chandra, Daryus
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Babar, Zunaira
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Nguyen, Hung
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Alanis, Dimitrios
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Botsinis, Panagiotis
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Ng, Soon
e19a63b0-0f12-4591-ab5f-554820d5f78c
Hanzo, Lajos
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Chandra, Daryus
a2f091a8-9772-4633-8e3b-d3220b10a2ec
Babar, Zunaira
23ede793-1796-449d-b5aa-93a297e5677a
Nguyen, Hung
6f5a71ef-ea98-49e0-9be7-7f5bb9880f52
Alanis, Dimitrios
8ae8ead6-3974-4886-8e17-1b4bff1d94e0
Botsinis, Panagiotis
d7927fb0-95ca-4969-9f8c-1c0455524a1f
Ng, Soon
e19a63b0-0f12-4591-ab5f-554820d5f78c
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1

Chandra, Daryus, Babar, Zunaira, Nguyen, Hung, Alanis, Dimitrios, Botsinis, Panagiotis, Ng, Soon and Hanzo, Lajos (2017) Quantum coding bounds and a closed-form approximation of the minimum distance versus quantum coding rate. IEEE Access, 5, 11557-11581. (doi:10.1109/ACCESS.2017.2716367).

Record type: Article

Abstract

The trade-off between the quantum coding rate and the associated error correction capability is characterized by the quantum coding bounds. The unique solution for this trade-off 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 trade-off between the quantum coding rate and the minimum distance of quantum stabilizer codes. For example, for a half-rate quantum stabilizer code having a codeword 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.

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QuantumCodingBounds - Accepted Manuscript
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More information

Accepted/In Press date: 8 June 2017
e-pub ahead of print date: 16 June 2017
Organisations: Electronics & Computer Science, Southampton Wireless Group

Identifiers

Local EPrints ID: 411906
URI: https://eprints.soton.ac.uk/id/eprint/411906
PURE UUID: 98062877-e94d-4ed0-ba3e-f4b633ea4954
ORCID for Daryus Chandra: ORCID iD orcid.org/0000-0003-2406-7229
ORCID for Zunaira Babar: ORCID iD orcid.org/0000-0002-7498-4474
ORCID for Hung Nguyen: ORCID iD orcid.org/0000-0001-6349-1044
ORCID for Dimitrios Alanis: ORCID iD orcid.org/0000-0002-6654-1702
ORCID for Soon Ng: ORCID iD orcid.org/0000-0002-0930-7194
ORCID for Lajos Hanzo: ORCID iD orcid.org/0000-0002-2636-5214

Catalogue record

Date deposited: 29 Jun 2017 16:31
Last modified: 14 Mar 2019 01:55

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