Abstract. We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions that are powers of primes is presented. It is also proved that in any dimension d the number of mutually unbiased bases is at most d+1 . An explicit representation of mutually unbiased observables in terms of Pauli matrices are provided for d=2m .
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Bandyopadhyay, ., Boykin, ., Roychowdhury, . et al. A New Proof for the Existence of Mutually Unbiased Bases . Algorithmica 34, 512–528 (2002). https://doi.org/10.1007/s00453-002-0980-7
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DOI: https://doi.org/10.1007/s00453-002-0980-7