Mutually unbiased bases in dimension six containing a product-vector basis

被引：0
作者：
Lin Chen
Li Yu
机构：
[1] Beihang University,School of Mathematics and Systems Science
[2] Beihang University,International Research Institute for Multidisciplinary Science
[3] Hangzhou Normal University,Department of Physics
来源：
Quantum Information Processing | 2018年 / 17卷
关键词：
Mutually unbiased bases; Quantum tomography; Quantum cryptography;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Excluding the existence of four MUBs in C6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}^6$$\end{document} is an open problem in quantum information. We investigate the number of product-vectors in the set of four mutually unbiased bases (MUBs) in dimension six, by assuming that the set exists and contains a product-vector basis. We show that in most cases the number of product-vectors in each of the remaining three MUBs is at most two. We further construct the exceptional case in which the three MUBs respectively contain at most three, two and two product-vectors. We also investigate the number of vectors mutually unbiased to an orthonormal basis.
引用
收藏
相关论文
共 36 条
  • [1] Brierley S(2008)Maximal sets of mutually unbiased quantum states in dimension 6 Phys. Rev. A 78 042312-undefined
  • [2] Weigert S(2009)Constructing mutually unbiased bases in dimension six Phys. Rev. A 79 052316-undefined
  • [3] Brierley S(2010)Mutually unbiased bases and semi-definite programming J. Phys. Conf. Ser. 254 012008-undefined
  • [4] Weigert S(2010)On mutually unbiased bases Int. J. Quantum Inf. 8 535-undefined
  • [5] Brierley S(2012)On the impossibility to extend triples of mutually unbiased product bases in dimension six Int. J. Quantum Inf. 10 1250056-undefined
  • [6] Weigert S(2011)Mutually unbiased bases in six dimensions: the four most distant bases Phys. Rev. A 83 062303-undefined
  • [7] Durt T(2015)On properties of Karlsson Hadamards and sets of mutually unbiased bases in dimension six Linear Algebra Appl. 466 296-undefined
  • [8] Englert B-G(2017)Small sets of complementary observables Phys. Rev. A 95 012118-undefined
  • [9] Bengtsson I(2013)All unitaries having operator Schmidt rank 2 are controlled unitaries Phys. Rev. A 87 022329-undefined
  • [10] Zyczkowski K(2014)Nonlocal and controlled unitary operators of Schmidt rank three Phys. Rev. A 89 062326-undefined
1234