Mutually Unbiased Bases and Orthogonal Latin Squares

Published 5 Nov 2025 in quant-ph | (2511.03537v1)

Abstract: In this paper, we prove that the existence of a complete set of mutually unbiased bases (MUBs) in N-dimensional Hilbert space implies the existence of a complete set of mutually orthogonal Latin squares (MOLSs) of order N. In particular, we prove that a complete set of MUBs does not exist in dimension six (the first dimension which is not a power of prime).

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Stefan Joka

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