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MORE CONSTRUCTIONS OF APPROXIMATELY MUTUALLY UNBIASED BASES

Part of: Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  17 August 2015

XIWANG CAO  and
WUN-SENG CHOU
XIWANG CAO*
Affiliation:
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, PR China email [email protected]
WUN-SENG CHOU
Affiliation:
Institute of Mathematics, Academia Sinica, Taiwan Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan email [email protected]
*
✉[email protected]
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Abstract

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Let $m$ be a positive integer and $p$ a prime number. We prove the orthogonality of some character sums over the finite field $\mathbb{F}_{p^{m}}$ or over a subset of a finite field and use this to construct some new approximately mutually unbiased bases of dimension $p^{m}$ over the complex number field $\mathbb{C}$, especially with $p=2$.

Keywords

finite fieldcharacter sumapproximately mutually unbiased basesquantum information theory

MSC classification

Primary: 11T71: Algebraic coding theory; cryptography
Secondary: 81P70: Quantum coding (general)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 2 , April 2016 , pp. 211 - 222
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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