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Isolated Hadamard Matrices from Mutually Unbiased Product Bases

Published 5 Aug 2012 in math-ph, math.MP, and quant-ph | (1208.1057v2)

Abstract: A new construction of complex Hadamard matrices of composite order d=pq, with primes p,q, is presented which is based on pairs of mutually unbiased bases containing only product states. For product dimensions d < 100, we illustrate the method by deriving many previously unknown complex Hadamard matrices. We obtain at least 12 new isolated matrices of Butson type, with orders ranging from 9 to 91.

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