Experimental adaptive quantum state tomography based on rank-preserving transformations

TL;DR

This paper introduces an adaptive quantum state tomography method based on rank-preserving transformations, demonstrating its effectiveness through numerical and experimental comparisons with other adaptive and random-basis methods.

Contribution

It presents a novel adaptive tomography approach utilizing rank-preserving transformations, with improvements via transformation unitary freedom and measurement set complementation.

Findings

Rank-preserving tomography shows high accuracy and fast convergence.

The method outperforms some existing adaptive and random-basis techniques.

Experimental results validate the numerical simulations.

Abstract

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.