Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies

TL;DR

This paper reviews and enhances scalable methods for partial quantum process tomography using twirling techniques, clarifying their significance and proposing improvements for more efficient quantum map characterization.

Contribution

It unifies existing approaches, introduces extensions and improvements, and clarifies the role of the $oldsymbol{ extchi}$-matrix in scalable quantum process tomography.

Findings

Enhanced methods for partial quantum process tomography.

Comparative analysis of different twirling-based approaches.

Clarified the significance of the $oldsymbol{ extchi}$-matrix in quantum map characterization.

Abstract

We present in a unified manner the existing methods for scalable partial quantum process tomography. We focus on two main approaches: the one presented in Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)], and the ones described, respectively, in Emerson et al. [Science 317, 1893 (2007)] and L\'{o}pez et al. [Phys. Rev. A 79, 042328 (2009)], which can be combined together. The methods share an essential feature: They are based on the idea that the tomography of a quantum map can be efficiently performed by studying certain properties of a twirling of such a map. From this perspective, in this paper we present extensions, improvements and comparative analyses of the scalable methods for partial quantum process tomography. We also clarify the significance of the extracted information, and we introduce interesting and useful properties of the $\chi$-matrix representation of quantum maps that can be used to establish a clearer path toward achieving full tomography of quantum processes in a scalable way.