Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1310.8347

Quantum Imaging of High-Dimensional Hilbert Spaces with Radon Transform

László Gyöngyösi

Published Oct 30, 2013• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1310.8347

Related papers

Quantum imaging of high‐dimensional Hilbert spaces with Radon transform

László Gyöngyösi

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.

International Journal of Circuit Theory and Applications•Mar 15, 2017•14 citations

Quantum Imaging of High-Dimensional Hilbert Spaces with Radon Transform

László Gyöngyösi

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.

Frontiers in Optics•Jan 1, 2014•2 citations

Quantum Holographic Communication via Holographic Entanglement Networks

Urvi Sinha, Souvik Mukherjee, Sumit Kumar Jindal

This study investigates quantum holography, emphasizing its capability to conduct holographic imaging without the requirement for first-order coherence—a limitation of classical physics. By harnessing quantum entanglement, where image data is embedded in the phase correlation of polarization-entangled photon pairs and spread across the transverse spatial dimension, quantum holography enhances imaging performance. This technique not only improves resolution for polarization-sensitive phase objects but also provides resilience against stochastic phase fluctuations and uncontrolled ambient light, offering significant tangible benefits compared to conventional holography. Additionally, its integration with quantum tomography enables precise analysis of multi-dimensional hyper-entangled states, advancing quantum state analysis. Although current challenges remain, such as extended acquisition times due to technological constraints, ongoing advancements in faster, more affordable sensors are expected to address these issues. As a result, quantum holography is poised to have broad applications in biological imaging, sensing, and the exploration of complex high-dimensional quantum states. These developments position quantum holography as a crucial technology in the future of quantum optical communication and information processing, driving innovation and opening new avenues in these fields.

International Conference on Control, Communication and Computing (ICCC)•May 23, 2025•0 citations

Quantifying entanglement in a 68-billion-dimensional quantum state space

James Schneeloch, Christopher C. Tison, Michael L. Fanto +2 more

Abstract Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which demands an intractable number of measurements even for modestly-sized systems. Here we demonstrate a method for rigorously quantifying high-dimensional entanglement from extremely limited data. We improve an entropic, quantitative entanglement witness to operate directly on compressed experimental data acquired via an adaptive, multilevel sampling procedure. Only 6,456 measurements are needed to certify an entanglement-of-formation of 7.11 ± .04 ebits shared by two spatially-entangled photons. With a Hilbert space exceeding 68 billion dimensions, we need 20-million-times fewer measurements than the uncompressed approach and 1018-times fewer measurements than tomography. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.

arXiv:1804.04515•Nature Communications•Jun 25, 2019•55 citations

High-accuracy adaptive quantum tomography for high-dimensional quantum systems

Luciano Pereira, Daniel Martínez, Gustavo Cañas +4 more

The accuracy of estimating $d$-dimensional quantum states is limited by the Gill-Massar bound. It can be saturated in the qubit ($d=2$) scenario using adaptive standard quantum tomography. In higher dimensions, however, this is not the case and the accuracy achievable with adaptive quantum tomography quickly deteriorates with increasing $d$. Moreover, it is not known whether or not the Gill-Massar bound can be reached for an arbitrary $d$. To overcome this limitation, we introduce an adaptive tomographic method that is characterized by a precision that is better than half that of the Gill-Massar bound for any finite dimension. This provides a new achievable accuracy limit for quantum state estimation. We demonstrate the high-accuracy of our method by estimating the state of 10-dimensional quantum systems. With the advent of new technologies capable of high-dimensional quantum information processing, our results become critically relevant as state reconstruction is an essential tool for certifying the proper operation of quantum devices.

arXiv:2009.04791•Sep 10, 2020•0 citations

Quantifying Entanglement in a 68-billion Dimensional Quantum State Space

James Schneeloch, Christopher C. Tison, Michael L. Fanto +2 more

Abstract Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which demands an intractable number of measurements even for modestly-sized systems. Here we demonstrate a method for rigorously quantifying high-dimensional entanglement from extremely limited data. We improve an entropic, quantitative entanglement witness to operate directly on compressed experimental data acquired via an adaptive, multilevel sampling procedure. Only 6, 456 measurements are needed to certify an entanglement-of-formation of 7.11 ± .04 ebits shared by two spatially-entangled photons. With a Hilbert space exceeding 68 billion dimensions, we need 20-million-times fewer measurements than the uncompressed approach and 1018-times fewer measurements than tomography. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.

•Jun 25, 2019•44 citations
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.
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.
This study investigates quantum holography, emphasizing its capability to conduct holographic imaging without the requirement for first-order coherence—a limitation of classical physics. By harnessing quantum entanglement, where image data is embedded in the phase correlation of polarization-entangled photon pairs and spread across the transverse spatial dimension, quantum holography enhances imaging performance. This technique not only improves resolution for polarization-sensitive phase objects but also provides resilience against stochastic phase fluctuations and uncontrolled ambient light, offering significant tangible benefits compared to conventional holography. Additionally, its integration with quantum tomography enables precise analysis of multi-dimensional hyper-entangled states, advancing quantum state analysis. Although current challenges remain, such as extended acquisition times due to technological constraints, ongoing advancements in faster, more affordable sensors are expected to address these issues. As a result, quantum holography is poised to have broad applications in biological imaging, sensing, and the exploration of complex high-dimensional quantum states. These developments position quantum holography as a crucial technology in the future of quantum optical communication and information processing, driving innovation and opening new avenues in these fields.
Abstract Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which demands an intractable number of measurements even for modestly-sized systems. Here we demonstrate a method for rigorously quantifying high-dimensional entanglement from extremely limited data. We improve an entropic, quantitative entanglement witness to operate directly on compressed experimental data acquired via an adaptive, multilevel sampling procedure. Only 6,456 measurements are needed to certify an entanglement-of-formation of 7.11 ± .04 ebits shared by two spatially-entangled photons. With a Hilbert space exceeding 68 billion dimensions, we need 20-million-times fewer measurements than the uncompressed approach and 1018-times fewer measurements than tomography. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.
The accuracy of estimating ddd-dimensional quantum states is limited by the Gill-Massar bound. It can be saturated in the qubit (d=2d=2d=2) scenario using adaptive standard quantum tomography. In higher dimensions, however, this is not the case and the accuracy achievable with adaptive quantum tomography quickly deteriorates with increasing ddd. Moreover, it is not known whether or not the Gill-Massar bound can be reached for an arbitrary ddd. To overcome this limitation, we introduce an adaptive tomographic method that is characterized by a precision that is better than half that of the Gill-Massar bound for any finite dimension. This provides a new achievable accuracy limit for quantum state estimation. We demonstrate the high-accuracy of our method by estimating the state of 10-dimensional quantum systems. With the advent of new technologies capable of high-dimensional quantum information processing, our results become critically relevant as state reconstruction is an essential tool for certifying the proper operation of quantum devices.
Abstract Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which demands an intractable number of measurements even for modestly-sized systems. Here we demonstrate a method for rigorously quantifying high-dimensional entanglement from extremely limited data. We improve an entropic, quantitative entanglement witness to operate directly on compressed experimental data acquired via an adaptive, multilevel sampling procedure. Only 6, 456 measurements are needed to certify an entanglement-of-formation of 7.11 ± .04 ebits shared by two spatially-entangled photons. With a Hilbert space exceeding 68 billion dimensions, we need 20-million-times fewer measurements than the uncompressed approach and 1018-times fewer measurements than tomography. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.