New construction of two kinds of approximate unbiased bases

Journal of Civil Aviation University of China ›› 2022, Vol. 40 ›› Issue (6): 60-64.

• Basic Science • Previous Articles

New construction of two kinds of approximate unbiased bases

XU Dengming^a , LI Feiya^b

(a. Sino-European Institute of Aviation Engineering; b. College of Science, CAUC, Tianjin 300300, China)

Received:2021-01-22 Revised:2021-04-27 Online:2022-12-10 Published:2023-10-26

Abstract

Abstract: Mutually unbiased bases are the main topics in quantum information theory. In general, it is difficult to determine the maximal number of mutually unbiased bases over a finite dimensional complex vector space. For this reason, mutually unbiased bases with relaxed inner product conditions, the so called approximately mutually unbiased bases, have been gradually considered. Exponential sums over finite fields play an important role in the construction of approximately mutually unbiased bases. In this paper, two new approximately mutually unbiased bases are constructed using two kinds of exponential sums over finite fields.

Key words: approximately mutually unbiased bases, finite field, Gauss sums, Jacobi sums

CLC Number:

O413

XU Dengming , LI Feiya. New construction of two kinds of approximate unbiased bases[J]. Journal of Civil Aviation University of China, 2022, 40(6): 60-64.

References

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New construction of two kinds of approximate unbiased bases

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