Frontiers in Optics

Quantum Imaging of High-Dimensional Hilbert Spaces with Radon Transform

László Gyöngyösi

Published Jan 1, 2014• 2 citations

Abstract

We introduce a post-processing method for quantum imaging that is based on the Radon transform. We show that the entropic separability bound is violated considerably more strongly in comparison to the standard setting.

DOI: 10.1364/fio.2014.jtu3a.26

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Summary High‐dimensional Hilbert spaces possess large information encoding and transmission capabilities. Characterizing exactly the real potential of high‐dimensional entangled systems is a cornerstone of tomography and quantum imaging. The accuracy of the measurement apparatus and devices used in quantum imaging is physically limited, which allows no further improvements to be made. To extend the possibilities, we introduce a post‐processing method for quantum imaging that is based on the Radon transform and the projection‐slice theorem. The proposed solution leads to an enhanced precision and a deeper parameterization of the information conveying capabilities of high‐dimensional Hilbert spaces. We demonstrate the method for the analysis of high‐dimensional position–momentum photonic entanglement. We show that the entropic separability bound in terms of standard deviations is violated considerably more strongly in comparison to the standard setting and current data processing. The results indicate that the possibilities of the quantum imaging of high‐dimensional Hilbert spaces can be extended by applying appropriate calculations in the post‐processing phase. Copyright © 2017 John Wiley & Sons, Ltd.

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Preface

This special issue is devoted to Quantum Imaging, a very interesting and actively developing area of quantum physics and quantum optics research. The majority of papers in this issue are based on p...

Journal of Modern OpticsFeb 21, 20064 citations

1 Normal Completely Positive Maps on the Space of Quantum Operations

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Quantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps transforming quantum operations with input in a separable von Neumann algebra and output in the algebra of the bounded operators on a given separable Hilbert space. In this setting we prove two dilation theorems for quantum supermaps that are the analogues of the Stinespring and Radon-Nikodym theorems for quantum operations. Finally, we consider the case of quantum superinstruments, namely measures with values in the set of quantum supermaps, and derive a dilation theorem for them that is analogue to Ozawa's theorem for quantum instruments. The three dilation theorems presented here show that all the supermaps defined in this paper can be implemented by connecting devices in quantum circuits.

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