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Akin to the idea of complete sets of mutually unbiased bases for prime-dimensional Hilbert spaces, $$\mathcal {H}_d$$ Hd , we study its analogue for a d-dimensional subspace of $$M (d,\mathbb {C})$$ M(d,C) , i.e. mutually unbiased unitary bases (MUUBs) comprising of unitary operators. We note an obvious isomorphism between the vector spaces and beyond that, we define a relevant monoid structure for...
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