Quantum tomography is a process of quantum state reconstruction using data from multiple measurements. An essential goal for a quantum tomography algorithm is to find measurements that will maximize the useful information about an unknown quantum state obtained through measurements. One of the recently proposed methods of quantum tomography is the algorithm based on rank-preserving transformations. The main idea is to transform a basic measurement set in a way to provide a situation that is equivalent to measuring the maximally mixed state. As long as tomography of a fully mixed state has the fastest convergence comparing to other states, this method is expected to be highly accurate. We present numerical and experimental comparisons of rank-preserving tomography with another adaptive method, which includes measurements in the estimator eigenbasis and with random-basis tomography. We also study ways to improve the efficiency of the rank-preserving transformations method using transformation unitary freedom and measurement set complementation.

中文翻译：

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基于保阶变换的实验自适应量子态断层扫描

量子断层扫描是使用来自多次测量的数据重建量子态的过程。量子断层扫描算法的一个基本目标是找到可以最大化有关通过测量获得的未知量子态的有用信息的测量值。最近提出的量子断层扫描方法之一是基于秩保持变换的算法。主要思想是以某种方式转换基本测量集，以提供等效于测量最大混合状态的情况。只要完全混合状态的断层扫描与其他状态相比具有最快的收敛性，该方法就有望具有高度的准确性。我们提出了保秩断层扫描与另一种自适应方法的数值和实验比较，其中包括估计器本征基础和随机基础断层扫描中的测量。我们还研究了使用变换幺正自由度和测量集互补来提高保秩变换方法效率的方法。