Enhancing multi-step quantum state tomography by PhaseLift

TL;DR

This paper introduces an enhanced adaptive quantum state tomography method using a new sampling scheme and PhaseLift, significantly improving accuracy and reducing storage needs for multi-photon quantum systems.

Contribution

It develops a three-step adaptive tomography approach with a novel sampling scheme and applies PhaseLift to optimize measurement storage, advancing quantum state reconstruction techniques.

Findings

Mean square error improved from 10^{-4} to 10^{-9}

Enhanced accuracy with fewer copies of quantum states

Reduced storage space for measurement operators

Abstract

Multi-photon system has been studied by many groups, however the biggest challenge faced is the number of copies of an unknown state are limited and far from detecting quantum entanglement. The difficulty to prepare copies of the state is even more serious for the quantum state tomography. One possible way to solve this problem is to use adaptive quantum state tomography, which means to get a preliminary density matrix in the first step and revise it in the second step. In order to improve the performance of adaptive quantum state tomography, we develop a new distribution scheme of samples and extend it to three steps, that is to correct it once again based on the density matrix obtained in the traditional adaptive quantum state tomography. Our numerical results show that the mean square error of the reconstructed density matrix by our new method is improved to the level from $10^{-4}$ to $10^{-9}$ for several tested states. In addition, PhaseLift is also applied to reduce the required storage space of measurement operator.