2004/07/12 by Paweł Wocjan, Pawel Wocjan, Wocjan, Pawel +2 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Physical sciences #Quantum Physics (quant-ph) #graph theory and CDMA systems #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0407081
10 pages
arxiv created 2004/07/12 · openalex publication_date 2004/07/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that k=w+2 mutually unbiased bases can be constructed in any square dimension d=s2 provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (k,s)-nets (which can be constructed from w mutually orthogonal Latin squares of order s and vice versa) and generalized Hadamard matrices of size s. Using known lower bounds on the asymptotic growth of the number of mutually orthogonal Latin squares (based on number theoretic sieving techniques), we obtain that the number of mutually unbiased bases in dimensions d=s2 is greater than s1/14.8 for all s but finitely many exceptions. Furthermore, our construction gives more mutually orthogonal bases in many non-prime-power dimensions than the construction that reduces the problem to prime power dimensions.