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New Journal of Physics

Focus on quantum tomography

Konrad Banaszek, M. Cramer, D Gross

Published Dec 13, 2013• 105 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/15/12/125020

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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.
The Wigner function was formulated in 1932 by Eugene Paul Wigner, at a time when quantum mechanics was in its infancy. In doing so, he brought phase space representations into quantum mechanics. However, its unique nature also made it very interesting for classical approaches and for identifying the deviations from classical behavior and the entanglement that can occur in quantum systems. What stands out, though, is the feature to experimentally reconstruct the Wigner function, which provides far more information on the system than can be obtained by any other quantum approach. This feature is particularly important for the field of quantum information processing and quantum physics. However, the Wigner function finds wide-ranging use cases in other dominant and highly active fields as well, such as in quantum electronics—to model the electron transport, in quantum chemistry—to calculate the static and dynamical properties of many-body quantum systems, and in signal processing—to investigate waves passing through certain media. What is peculiar in recent years is a strong increase in applying it: Although originally formulated 86 years ago, only today the full potential of the Wigner function—both in ability and diversity—begins to surface. This review, as well as a growing, dedicated Wigner community, is a testament to this development and gives a broad and concise overview of recent advancements in different fields.
Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This 'focus on' collection brings together several of the latest developments in the field and facilitates the synergy between different approaches.
Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This 'focus on' collection brings together several of the latest developments in the field and facilitates the synergy between different approaches.