Quantum codes from Hadamard matrices

W. F. Ke; K. F. Lai; R. B. Zhang

doi:10.1080/03081080903062121

Quantum codes from Hadamard matrices

W. F. Ke, K. F. Lai, R. B. Zhang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

From each q × q unitary matrix Φ, we construct a family of quantum codes C_t(Φ), t ≥ 1, for q-state systems which encode (2t + 1)² q-states into one q-state. We show that such codes are capable of correcting the errors of weight up to t if and only if Φ is a complex Hadamard matrix.

Original language	English
Pages (from-to)	847-854
Number of pages	8
Journal	Linear and Multilinear Algebra
Volume	58
Issue number	7
DOIs	https://doi.org/10.1080/03081080903062121
Publication status	Published - 2010

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1080/03081080903062121

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title = "Quantum codes from Hadamard matrices",

abstract = "From each q × q unitary matrix Φ, we construct a family of quantum codes Ct(Φ), t ≥ 1, for q-state systems which encode (2t + 1)2 q-states into one q-state. We show that such codes are capable of correcting the errors of weight up to t if and only if Φ is a complex Hadamard matrix.",

author = "Ke, {W. F.} and Lai, {K. F.} and Zhang, {R. B.}",

note = "Funding Information: W.F. Ke was partially supported by The National Science Council, Taiwan, under grants NSC-94-2115-M-006-008 and NSC-95-2115-M-006-004.",

year = "2010",

doi = "10.1080/03081080903062121",

language = "English",

volume = "58",

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journal = "Linear and Multilinear Algebra",

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publisher = "Taylor and Francis Ltd.",

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TY - JOUR

T1 - Quantum codes from Hadamard matrices

AU - Ke, W. F.

AU - Lai, K. F.

AU - Zhang, R. B.

N1 - Funding Information: W.F. Ke was partially supported by The National Science Council, Taiwan, under grants NSC-94-2115-M-006-008 and NSC-95-2115-M-006-004.

PY - 2010

Y1 - 2010

N2 - From each q × q unitary matrix Φ, we construct a family of quantum codes Ct(Φ), t ≥ 1, for q-state systems which encode (2t + 1)2 q-states into one q-state. We show that such codes are capable of correcting the errors of weight up to t if and only if Φ is a complex Hadamard matrix.

AB - From each q × q unitary matrix Φ, we construct a family of quantum codes Ct(Φ), t ≥ 1, for q-state systems which encode (2t + 1)2 q-states into one q-state. We show that such codes are capable of correcting the errors of weight up to t if and only if Φ is a complex Hadamard matrix.

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U2 - 10.1080/03081080903062121

DO - 10.1080/03081080903062121

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AN - SCOPUS:77956825587

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VL - 58

SP - 847

EP - 854

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 7

ER -

Quantum codes from Hadamard matrices

Abstract

All Science Journal Classification (ASJC) codes

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