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On the hardnesses of several quantum decoding problems.

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Titel: On the hardnesses of several quantum decoding problems.
Autoren: Kuo, Kao-Yueh, Lu, Chung-Chin
Quelle: Quantum Information Processing; Apr2020, Vol. 19 Issue 4, p1-17, 17p
Schlagwörter: QUANTUM cryptography, ERROR probability, DECODING algorithms, HARDNESS, DEFINITIONS
Abstract: We classify the time complexities of three decoding problems for quantum stabilizer codes: quantum bounded distance decoding (QBDD), quantum maximum likelihood decoding (QMLD), and quantum minimum error probability decoding (QMEPD). For QBDD, we show that it is NP-hard based on Fujita's result, and cover the gap of full row rank of check matrices, like what Berlekamp, McEliece, and Tilborg suggested in 1978. Then, we give some insight into the quantum decoding problems to clarify that the degeneracy property is implicitly embedded in any decoding algorithm, independent of the typical definition of degenerate codes. Then, over the depolarizing channel model, we show that QMLD and QMEPD are NP-hard. The NP-hardnesses of these decoding problems indicate that decoding general stabilizer codes is extremely difficult, strengthening the foundation of quantum code-based cryptography. [ABSTRACT FROM AUTHOR]
Copyright of Quantum Information Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: On the hardnesses of several quantum decoding problems.
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  Data: <searchLink fieldCode="AR" term="%22Kuo%2C+Kao-Yueh%22">Kuo, Kao-Yueh</searchLink><br /><searchLink fieldCode="AR" term="%22Lu%2C+Chung-Chin%22">Lu, Chung-Chin</searchLink>
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  Data: Quantum Information Processing; Apr2020, Vol. 19 Issue 4, p1-17, 17p
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  Data: <searchLink fieldCode="DE" term="%22QUANTUM+cryptography%22">QUANTUM cryptography</searchLink><br /><searchLink fieldCode="DE" term="%22ERROR+probability%22">ERROR probability</searchLink><br /><searchLink fieldCode="DE" term="%22DECODING+algorithms%22">DECODING algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22HARDNESS%22">HARDNESS</searchLink><br /><searchLink fieldCode="DE" term="%22DEFINITIONS%22">DEFINITIONS</searchLink>
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  Data: We classify the time complexities of three decoding problems for quantum stabilizer codes: quantum bounded distance decoding (QBDD), quantum maximum likelihood decoding (QMLD), and quantum minimum error probability decoding (QMEPD). For QBDD, we show that it is NP-hard based on Fujita's result, and cover the gap of full row rank of check matrices, like what Berlekamp, McEliece, and Tilborg suggested in 1978. Then, we give some insight into the quantum decoding problems to clarify that the degeneracy property is implicitly embedded in any decoding algorithm, independent of the typical definition of degenerate codes. Then, over the depolarizing channel model, we show that QMLD and QMEPD are NP-hard. The NP-hardnesses of these decoding problems indicate that decoding general stabilizer codes is extremely difficult, strengthening the foundation of quantum code-based cryptography. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Quantum Information Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s11128-020-02622-8
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        Text: English
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      – SubjectFull: QUANTUM cryptography
        Type: general
      – SubjectFull: ERROR probability
        Type: general
      – SubjectFull: DECODING algorithms
        Type: general
      – SubjectFull: HARDNESS
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              Text: Apr2020
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