论文标题
$ d $二维的希尔伯特空间上的运营商相互无偏的统一基础
Mutually Unbiased Unitary Bases of Operators on $d$-dimensional Hilbert Space
论文作者
论文摘要
类似于希尔伯特空间的相互无偏基底座的概念，我们考虑了运算符空间的互无偏见基地（MUUB），$ m（d，\ mathbb {c}）$，作用于这样的希尔伯特空间。 Muub的概念反映了一个$ m（d，\ m athbb {c}）$的统一猜测，当估计另一个统一运算符时。但是，对于Prime dimension $ d $，已知Muubs的最大数量为$ d^{2} -1 $，假设它们存在，则没有已知的构造配方。但是，始终可以构建至少三个MUUB，并且最大数字的范围非常大的$ d $。 MUUBS也可以以$ M（d，\ Mathbb {C}）$为$ D $二维子空间存在，最大数字为$ D $。
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 $d$.
