Mutually unbiased frames
Mutually unbiased frames
复制标题
互不偏向的框架
DOI：
10.22331/q-2022-11-03-851
复制
发表时间：
2021
期刊：
影响因子：
6.4
通讯作者：
D. Goyeneche
中科院分区：
文献类型：
--
作者：
Felipe Pérez;V. G. Avella;D. Goyeneche
在这项工作中，相互无偏框架的概念被引入作为线性无关和规范化向量组成的集合的无偏性的最一般的概念。它包含了已经存在的概念unbiasedness正交基，定期单纯形，等角紧框架，积极的运营商价值的措施，也包括对称信息完全量子测量。在引入该工具之后，通过找到关于最后提到的星座类的以下结果来显示其能力：（i）真实的基准状态不存在于任何偶数维度中，以及（ii）未知的d维基准状态被参数化，先验地，仅具有大约3d/2真实的变量，而不失一般性。此外，多参数族的纯量子态具有最小的不确定性方面的几个选择的d+1正交基示出，在每个维度d。这些最后的家庭包含在每个有限维的所有现有的基准状态，和基地包括最大集的d+1相互无偏基地，当d是一个素数。
In this work, the concept of mutually unbiased frames is introduced as the most general notion of unbiasedness for sets composed by linearly independent and normalized vectors. It encompasses the already existing notions of unbiasedness for orthonormal bases, regular simplices, equiangular tight frames, positive operator valued measure, and also includes symmetric informationally complete quantum measurements. After introducing the tool, its power is shown by finding the following results about the last mentioned class of constellations: (i) real fiducial states do not exist in any even dimension, and (ii) unknown d-dimensional fiducial states are parameterized, a priori, with roughly 3d/2 real variables only, without loss of generality. Furthermore, multi-parametric families of pure quantum states having minimum uncertainty with regard to several choices of d+1 orthonormal bases are shown, in every dimension d. These last families contain all existing fiducial states in every finite dimension, and the bases include maximal sets of d+1 mutually unbiased bases, when d is a prime number.