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arXiv:1510.08140 · Physica Scripta

Quantum Tomography twenty years later

M. Asorey, Alberto Ibort, G Marmo, F Ventriglia

Published Jun 1, 2015• 56 citations
arXivHTMLPDF

Abstract

We show a sample of some relevant developments in classical and quantum tomography that have taken place over the last twenty years. We will present a general conceptual framework that provides a simple unifying mathematical picture for them and, as an effective use of it, three subjects have been chosen that offer a wide panorama of the scope of classical and quantum tomography: tomography along lines and submanifolds, coherent state tomography and tomography in the abstract algebraic setting of quantum systems.

DOI
10.1088/0031-8949/90/7/074031

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Quantum tomography has come a long way from early reconstructions of Wigner functions from projections along quadratures to the full characterization of multipartite systems. Now, it is routinely carried out in a wide variety of systems. And yet, many fundamental questions remain unanswered. In recent years, a spate of radical new experimental, theoretical and mathematical developments have occurred. The appeal of the subject lies largely in the breadth of techniques that must be brought together in order to fully understand the problem. This 'focus on' collection provides a platform for facilitating the exchange of ideas between the different communities involved in this process.
Latest developments in quantum tomography are presented. The method for measuring the state of radiation is derived in a simple group-theoretical framework that allows generalization to arbitrary quantum systems. Some recently developed topics are synthetically reviewed, including tomography of many radiation modes using only one local oscillator, generalization to TV-level systems, and new “adaptive” techniques for noise reduction. A set of newly proposed experiments is presented, based on a conditioned tomographic technique. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Engineering of quantum computers requires reliable characterization of qubits, quantum operations, and even the entire hardware. Quantum tomography is an indispensable framework in quantum characterization, verification, and validation (QCVV), which has been widely accepted by researchers. According to the tomographic target, quantum tomography can be categorized into quantum state tomography (QST), quantum process tomography (QPT), gate set tomography (GST), process tensor tomography (PTT), and instrument set tomography (IST). Standard quantum tomography toolkits generally consist of basic linear inverse methods and statistical maximum likelihood estimation (MLE) based methods. Furthermore, the performance of standard methods, including effectiveness and efficiency, has been further developed by exploiting Bayesian estimation, neural networks, matrix completion techniques, etc. In this review, we introduce the fundamental quantum tomography techniques, including QST, QPT, GST, PTT, and IST. We first introduce the details of basic linear inverse methods. Then, the framework of MLE methods with constraints is summarized. Finally, we briefly introduce recent further research in developing the performance of tomography. This review provides a primary getting-start in developing quantum tomography, which promotes quantum computer development.