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

• URL: http://arxiv.org/abs/2003.12201v1
• Date: Fri, 27 Mar 2020 01:41:03 GMT
• Title: Mutually Unbiased Unitary Bases of Operators on $d$-dimensional Hilbert Space
• Authors: Rinie N. M. Nasir, Jesni Shamsul Shaari, and Stefano Mancini
• Abstract summary: We consider mutually unbiased unitary bases (MUUB) for the space of operators, $M(d, mathbbC)$, acting on such Hilbert spaces. The notion of MUUB reflects the equiprobable guesses of unitary in one bases of $M(d, mathbbC)$ when estimating a unitary operator in another.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $d$.

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