Experimental adaptive quantum state tomography based on rank-preserving transformations

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 willmaximize the useful information about an unknown quantum state obtained throughmeasurements. One of the recently proposed methods of quantum tomography is the algorithmbased on rank-preserving transformations. The main idea is to transform a basic measurementset 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 toother states, this method is expected to be highly accurate. We present numerical andexperimental comparisons of rank-preserving tomography with another adaptive method, whichincludes measurements in the estimator eigenbasis and with random-basis tomography. We alsostudy ways to improve the efficiency of the rank-preserving transformations method using thetransformation unitary freedom and a measurement set complementation.