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We present in a unified manner the existing methods for scalable partialquantum process tomography. We focus on two main approaches: the one presentedin Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)], and the onesdescribed, respectively, in Emerson et al. [Science 317, 1893 (2007)] andL\'{o}pez et al. [Phys. Rev. A 79, 042328 (2009)], which can be combinedtogether. The methods share an essential feature: They are based on the ideathat the tomography of a quantum map can be efficiently performed by studyingcertain properties of a twirling of such a map. From this perspective, in thispaper we present extensions, improvements and comparative analyses of thescalable methods for partial quantum process tomography. We also clarify thesignificance of the extracted information, and we introduce interesting anduseful properties of the $\chi$-matrix representation of quantum maps that canbe used to establish a clearer path toward achieving full tomography of quantumprocesses in a scalable way.

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