New Constructions of Approximately Mutually Unbiased Bases by Character Sums over Galois Rings

DOI Web Site
  • GAO You
    School of Sciences, Civil Aviation University of China Tianjin Key Laboratory of Advanced Signal Processing, Civil Aviation University of China
  • XIE Ming-Yue
    School of Sciences, Civil Aviation University of China
  • WANG Gang
    School of Sciences, Civil Aviation University of China
  • SHEN Lin-Zhi
    School of Sciences, Civil Aviation University of China

抄録

<p>Mutually unbiased bases (MUBs) are widely used in quantum information processing and play an important role in quantum cryptography, quantum state tomography and communications. It's difficult to construct MUBs and remains unknown whether complete MUBs exist for any non prime power. Therefore, researchers have proposed the solution to construct approximately mutually unbiased bases (AMUBs) by weakening the inner product conditions. This paper constructs q AMUBs of ℂq, (q + 1) AMUBs of ℂq-1 and q AMUBs of ℂq-1 by using character sums over Galois rings and finite fields, where q is a power of a prime. The first construction of q AMUBs of ℂq is new which illustrates K AMUBs of ℂK can be achieved. The second and third constructions in this paper include the partial results about AMUBs constructed by W. Wang et al. in [9]. </p>

収録刊行物

キーワード

詳細情報 詳細情報について

問題の指摘

ページトップへ