2016/04/29 by Yanling Wang, Yan-Ling Wang, Wang, Yan-Ling +7
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cellular Automata and Applications #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #graph theory and CDMA systems #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1604.08665
6 pages, no figures
arxiv created 2016/04/29 · openalex publication_date 2016/04/29 · arxiv updated 2016/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the unextendible maximally entangled bases (UMEB) in ℂd\bigotimesℂd and connect it with the partial Hadamard matrix. Firstly, we show that for a given special UMEB in ℂd\bigotimesℂd, there is a partial Hadamard matrix can not extend to a complete Hadamard matrix in ℂd. As a corollary, any (d-1)× d partial Hadamard matrix can extend to a complete Hadamard matrix. Then we obtain that for any d there is an UMEB except d=p or 2p, where p≡ 3\mod 4 and p is a prime. Finally, we argue that there exist different kinds of constructions of UMEB in ℂnd\bigotimesℂnd for any n∈ ℕ and d=3×5 ×7.