Mutually unbiased bases

这个项目是建立在相互不偏不倚的基础上的，适用于具有一对以上连续变量的系统，例如位置和动量。对于具有复合维希尔伯特空间的量子系统，例如d=6，这样的基的最大数目是未知的。在具有多个自由度的无限维环境中，可以推导出复合维上相互无偏基的存在性问题的一个变种。它转化为在合适的实空间中寻找最大数量的向量，使得这些向量中的任何两个的辛积具有相同的值。对这一问题的解决将从一个新的视角来洞察长期存在的开放的存在问题。

This project is on mutually unbiased bases for systems with more than one pair of continuous variables such as position and momentum. For quantum systems with Hilbert spaces of composite dimensions such as d=6, the maximal number of such bases is not known. In the infinite-dimensional setting with more than one degree of freedom, a variant of the existence problem of mutually unbiased bases in composite dimensions can be formulated. It turns into a search for the maximal number of vectors in a suitable real space such that the symplectic products of any two of these vectors have the same value. A solution to this problem will offer insights into the long-standing open existence problem from a new perspective.