论文标题
与一户的超声预测相互交织
Orthogonal Projections on Hyperplanes Intertwined With Unitaries
论文作者
论文摘要
在有限维的复合矢量空间中固定一个点，并考虑在统一地图的组成下，与起点正交的正交投影的统一映射的组成序列。我们证明，通常，这些迭代的一系列平方规范总和到基础空间的尺寸。这使我们为量子系统构建了（依赖设备的）维度证人，这涉及在连续的是，不测量中获得某些结果的概率。在实际情况下，提供了本系列的确切公式，以及其在实际情况下的类似程序。
Fix a point in a finite-dimensional complex vector space and consider the sequence of iterates of this point under the composition of a unitary map with the orthogonal projection on the hyperplane orthogonal to the starting point. We prove that, generically, the series of the squared norms of these iterates sums to the dimension of the underlying space. This leads us to construct a (device-dependent) dimension witness for quantum systems which involves the probabilities of obtaining certain strings of outcomes in a sequential yes-no measurement. The exact formula for this series in non-generic cases is provided as well as its analogue in the real case.
