High-accuracy adaptive quantum tomography for high-dimensional quantum systems

TL;DR

This paper introduces an adaptive quantum tomography method that surpasses the Gill-Massar bound in accuracy for high-dimensional quantum systems, demonstrated on 10-dimensional states, advancing quantum state estimation capabilities.

Contribution

The authors develop a novel adaptive tomography technique that achieves better than half the Gill-Massar bound accuracy in any finite dimension, improving high-dimensional quantum state estimation.

Findings

Achieves precision better than half the Gill-Massar bound for any finite dimension.

Demonstrates high-accuracy state estimation on 10-dimensional quantum systems.

Provides a new fundamental accuracy limit for quantum state reconstruction.

Abstract

The accuracy of estimating $d$-dimensional quantum states is limited by the Gill-Massar bound. It can be saturated in the qubit ($d=2$) scenario using adaptive standard quantum tomography. In higher dimensions, however, this is not the case and the accuracy achievable with adaptive quantum tomography quickly deteriorates with increasing $d$. Moreover, it is not known whether or not the Gill-Massar bound can be reached for an arbitrary $d$. To overcome this limitation, we introduce an adaptive tomographic method that is characterized by a precision that is better than half that of the Gill-Massar bound for any finite dimension. This provides a new achievable accuracy limit for quantum state estimation. We demonstrate the high-accuracy of our method by estimating the state of 10-dimensional quantum systems. With the advent of new technologies capable of high-dimensional quantum information processing, our results become critically relevant as state reconstruction is an essential tool for certifying the proper operation of quantum devices.