Experimental adaptive quantum state tomography based on rank-preserving transformations

Abstract

Quantum tomography is a process of quantum state recognition with multiple measurements. An essential goal for the 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 the way to provide a situation that is equivalent to measuring the maximally mixed state. As long as the tomography of the 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 the transformation unitary freedom and a measurement set complementation.