Modern compressive tomography for quantum information science

TL;DR

This review introduces modern compressive tomography techniques developed since 2019 for efficiently characterizing low-rank quantum objects without prior assumptions, providing technical insights and numerical results for quantum information scientists.

Contribution

It offers a comprehensive survey of recent compressive tomography methods, including detailed explanations and numerical results, to aid adoption in quantum information science.

Findings

Efficient characterization of low-rank quantum states and processes.

Minimal measurement resources without prior assumptions.

Pedagogical presentation of theoretical and numerical results.

Abstract

This review serves as a concise introductory survey of modern compressive tomography developed since 2019. These are schemes meant for characterizing arbitrary low-rank quantum objects, be it an unknown state, a process or detector, using minimal measuring resources (hence compressive) without any \emph{a priori} assumptions (rank, sparsity, eigenbasis, \emph{etc}.) about the quantum object. This article contains a reasonable amount of technical details for the quantum-information community to start applying the methods discussed here. To facilitate the understanding of formulation logic and physics of compressive tomography, the theoretical concepts and important numerical results (both new and cross-referenced) shall be presented in a pedagogical manner.