Mutually Unbiased Unitary Bases of Operators on $d$-dimensional Hilbert Space

Abstract

Analogous to the notion of mutually unbiased bases for Hilbert spaces, we consider mutually unbiased unitary bases (MUUB) for the space of operators, $M(d,\mathbb{C})$, acting on such Hilbert spaces. The notion of MUUB reflects the equiprobable guesses of unitary in one bases of $M(d,\mathbb{C})$ when estimating a unitary operator in another. Though, for prime dimension $d$, the maximal number of MUUBs is known to be $d^2-1$, there is no known recipe for constructing them, assuming they exist. However, one can always construct a minimum of three MUUBs, and the maximal number is approached for very large values of $d$. MUUBs can also exists for some $d$-dimensional subspace of $M(d,\mathbb{C})$ with the maximal number being $d$.

11 pages, 1 figure

References in corpus (4)

• Optimizing quantum process tomography with unitary 2-designs
• Mutually unbiased bases and generalized Bell states
• On Mutually Unbiased Unitary Bases in prime dimensional Hilbert spaces
• Entropic Bounds For Unitary Testers and Mutually Unbiased Unitary Bases

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