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arXiv · 1811.07314

On Mutually Unbiased Unitary Bases in prime dimensional Hilbert spaces

Rinie N. M. Nasir·Jesni Shamsul Shaari·Stefano Mancini
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Abstract

Akin to the idea of complete sets of Mutually Unbiased Bases for prime dimensional Hilbert spaces, $\mathcal{H}_d$, we study its analogue for a $d$ dimensional subspace of $M (d,\mathbb{C})$, 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 $\mathcal{H}_d$ isomorphic to one for the subspace of $M (d,\mathbb{C})$. This provides us not only with the maximal number of such MUUBs, but also a recipe for its construction.

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Rinie N. M. Nasir, Jesni Shamsul Shaari, Stefano Mancini. 2019-03-22. On Mutually Unbiased Unitary Bases in prime dimensional Hilbert spaces. https://doi.org/10.1007/s11128-019-2298-2

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