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Construction of a Family of Maximally Entangled Bases in ℂd ⊗ ℂd′

Authors:	Chenghong Wang Kun Wang Zhu-Jun Zheng

Institution:	1.School of Mathematics, South China University of Technology, Guangzhou 510641, China;2.College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;3.Laboratory of Quantum Science and Engineering, South China University of Technology, Guangzhou 510641, China

Abstract:	In this paper, we present a new method for the construction of maximally entangled states in $C^{d} \otimes C^{d^{'}}$ when $d^{'} \geq 2 d$ . A systematic way of constructing a set of maximally entangled bases (MEBs) in $C^{d} \otimes C^{d^{'}}$ was established. Both cases when $d^{'}$ is divisible by d and not divisible by d are discussed. We give two examples of maximally entangled bases in $C^{2} \otimes C^{4}$ , which are mutually unbiased bases. Finally, we found a new example of an unextendible maximally entangled basis (UMEB) in $C^{2} \otimes C^{5}$ .

Keywords:	maximally entangled states mutually unbiased bases unextendible maximally entangled basis