On Mutually Unbiased Unitary Bases in prime dimensional Hilbert spaces

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.

Lemma 5 corrected, new appendixes B, D included, typos corrected

References in corpus (1)

• Optimizing quantum process tomography with unitary 2-designs

Cited by in corpus (3)

• Mutually Unbiased Unitary Bases of Operators on $d$-dimensional Hilbert Space
• Entropic Bounds For Unitary Testers and Mutually Unbiased Unitary Bases
• Entropic Bounds as Uncertainty Measure of Unitary Operators