Constructing Mutually Unbiased Bases from Unextendible Maximally Entangled Bases. Issue 1 (February 2020)

• Record Type: Journal Article
• Authors: Zhao, Hui; Zhang, Lin; Fei, Shao-Ming; Jing, Naihuan
• Is Part Of: Reports on mathematical physics. Volume 85:Issue 1(2020)
• Page Start: 105
• Page End: 118
• Publication Date: 2020-02
• Subjects: mutually unbiased bases -- unextendible maximally entangled bases -- unitary matrices; 03.67.Hk -- 03.65.Ud; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(20)30013-6
• Languages: English
• ISSNs: 0034-4877

Abstract

Abstract : We study mutually unbiased bases (MUBs) in which all the bases are unextendible maximally entangled ones. We first present a necessary and sufficient condition of constructing a pair of MUBs in C 2 ⊗ C 4 . Based on this condition, an analytical and necessary condition for constructing MUBs is given. Moreover we illustrate our approach by some detailed examples in C 2 ⊗ C 4 . The results are generalized to C 2 ⊗ C d ( d ≥ 3 ) and a concrete example in C 2 ⊗ C 8 is given.