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:1204.5758 · Physical Review Letters

Full-Field Quantum Correlations of Spatially Entangled Photons

Vsevolod Salakhutdinov, E. R. Eliel, W. Löffler

Published Apr 23, 2012• 124 citations
arXivHTMLPDF

Abstract

Spatially entangled twin photons allow the study of high-dimensional entanglement, and the Laguerre-Gauss modes are the most commonly used basis to discretize the single-photon mode spaces. In this basis, to date only the azimuthal degree of freedom has been investigated experimentally due to its fundamental and experimental simplicity. We show that the full spatial entanglement is indeed accessible experimentally; i.e., we have found practicable radial detection modes with negligible cross correlations. This allows us to demonstrate hybrid azimuthal-radial quantum correlations in a Hilbert space with more than 100 dimensions per photon.

DOI
10.1103/physrevlett.108.173604

Related papers

Entangled ripples and twists of light: radial and azimuthal Laguerre–Gaussian mode entanglement

Natalia Herrera Valencia, Vatshal Srivastav, Saroch Leedumrongwatthanakun +2 more

Abstract It is well known that photons can carry a spatial structure akin to a ‘twisted’ or ‘rippled’ wavefront. Such structured light fields have sparked significant interest in both classical and quantum physics, with applications ranging from dense communications to light–matter interaction. Harnessing the full advantage of transverse spatial photonic encoding using the Laguerre–Gaussian (LG) basis in the quantum domain requires control over both the azimuthal (twisted) and radial (rippled) components of photons. However, precise measurement of the radial photonic degree-of-freedom has proven to be experimentally challenging primarily due to its transverse amplitude structure. Here we demonstrate the generation and certification of full-field LG entanglement between photons pairs generated by spontaneous parametric down conversion in the telecom regime. By precisely tuning the optical system parameters for state generation and collection, and adopting recently developed techniques for precise spatial mode measurement, we are able to certify fidelities up to 85% and entanglement dimensionalities up to 26 in a 43-dimensional radial and azimuthal LG mode space. Furthermore, we study two-photon quantum correlations between nine LG mode groups, demonstrating a correlation structure related to mode group order and inter-modal cross-talk. In addition, we show how the noise-robustness of high-dimensional entanglement certification can be significantly increased by using measurements in multiple LG mutually unbiased bases. Our work demonstrates the potential offered by the full spatial structure of the two-photon field for enhancing technologies for quantum information processing and communication.

arXiv:2104.04506•Journal of Optics•Aug 25, 2021•23 citations

Radial Schmidt mode detector of entangled photons

Radhika Prasad, Nilakshi Senapati, Abhinandan Bhattacharjee +1 more

High-dimensional spatially entangled two-photon state generated by spontaneous parametric down-conversion process (SPDC) has become a promising resource for several quantum information science applications. For harnessing high-dimensional entanglement advantages, detection capability in the Schmidt basis is a necessity. Spatial entanglement has been explored in several modal bases, such as pixel, azimuthal, and radial modes. Among them, pixel and azimuthal entanglement have been widely utilized due to efficient access to their Schmidt modes, while radial-mode entanglement remains underexploited. This is because for radial coordinates, there is neither a Schmidt-decomposed form for the SPDC photons nor is there a technique for measuring high-dimensional radial Schmidt modes, which is a major roadblock in harnessing radial mode advantages. In this work, we first theoretically show that the azimuthal averaging of SPDC two-photon state yields a radial Schmidt-decomposed form under typical experimental situations. We then demonstrate an innovative approach for extracting the radial Schmidt modes and their spectrum by characterizing the density matrix in the radial basis of one of the SPDC photons. Finally, we report the first-ever measurement of radial Schmidt spectrum of upto 50 radial Schmidt modes with about 98\% fidelity.

quant-pharXiv:2606.25735•Jun 25, 2026•0 citations

Hybrid Radial-Angular Quantum Correlations of Spatially Entangled Photons

W. Löffler, Vsevolod Salakhutdinov, E. R. Eliel

We report the successful experimental exploration of the full transverse-mode space of spatially entangled photons, azimuthal and radial; and investigate theoretically and experimentally the subtle relation to the Schmidt eigenmodes of the downconverted twin photons.

Research in Optical Sciences•Jan 1, 2012•0 citations

Radial Schmidt mode detector of entangled photons

Radhika Prasad, Nilakshi Senapati, Abhinandan Bhattacharjee +1 more

Abstract High-dimensional spatially entangled two-photon states generated by the spontaneous parametric down-conversion process (SPDC) have become a promising resource for several quantum information science applications. In order to harness high-dimensional entanglement advantages, detection capability in the Schmidt basis is a necessity. Spatial entanglement has been explored in several modal bases, such as pixel, azimuthal, and radial modes. Among them, pixel and azimuthal entanglement have been widely utilized due to efficient access to their Schmidt modes, while radial-mode entanglement remains underexploited. This is due to radial coordinates not having a Schmidt-decomposed form for the SPDC photons or a technique for measuring high-dimensional radial Schmidt modes, which is a major roadblock in harnessing radial mode advantages. In this work, we first theoretically show that azimuthal averaging of SPDC two-photon states yields a radial Schmidt-decomposed form under typical experimental situations. We then demonstrate an innovative approach for extracting the radial Schmidt modes and their spectrum by characterizing the density matrix in the radial basis of one of the SPDC photons. Finally, we report the first-ever measurement of the radial Schmidt spectrum of up to 50 radial Schmidt modes with about 98% fidelity.

Journal of Optics•Jul 1, 2026•1 citation

High-dimensional Bell-state preparation and characterization based on single-photon radial and azimuthal mode multiplexing

Feng-Pei Li, Feng-Pei Li, Shiyue Jia +4 more

Laguerre–Gaussian (LG) modes are characterized by two integer parameters, p and l , which correspond to the radial and azimuthal modes of photons. Both degrees of freedom are discrete and high-dimensional, and each can be used to construct a high-dimensional Hilbert space. Here, we use the radial-azimuthal modes of a single photon to construct two-dimensional and four-dimensional Bell states and experimentally realize full single-photon Bell-state characterization, thereby verifying the orthogonality and completeness of the Bell states. Subsequently, we measure the magnitude and phase of a four-dimensional superposition state in a 16-dimensional Hilbert space, obtaining results in good agreement with theoretical predictions, which further confirms the completeness of the four-dimensional Bell basis. Our experiment demonstrates that the radial and azimuthal modes of a single photon play equally important roles. Multiplexing these two degrees of freedom enables the construction of higher-dimensional Hilbert spaces and significantly enhances the information-carrying capacity of a single photon. Our results hold potential applications in the development of quantum communication protocols with high channel capacity.

Photonics Research•Jun 22, 2026•0 citations

Full-mode characterization of correlated photon pairs generated in spontaneous downconversion

Alessio D’Errico, Felix Hufnagel, Filippo Miatto +2 more

Spontaneous parametric downconversion is the primary source to generate entangled photon pairs in quantum photonics laboratories. Depending on the experimental design, the generated photon pairs can be correlated in the frequency spectrum, polarization, position-momentum, and spatial modes. Exploring the spatial modes' correlation has hitherto been limited to the polar coordinates' azimuthal angle, and a few attempts to study Walsh mode's radial states. Here, we study the full-mode correlation, on a Laguerre-Gauss basis, between photon pairs generated in a type-I crystal. Furthermore, we explore the effect of a structured pump beam possessing different spatial modes onto bi-photon spatial correlation. Finally, we use the capability to project over arbitrary spatial mode superpositions to perform the bi-photon state's full quantum tomography in a 16-dimensional subspace.

arXiv:2103.08689•Optics Letters•Apr 19, 2021•21 citations
Spatially entangled twin photons allow the study of high-dimensional entanglement, and the Laguerre-Gauss modes are the most commonly used basis to discretize the single-photon mode spaces. In this basis, to date only the azimuthal degree of freedom has been investigated experimentally due to its fundamental and experimental simplicity. We show that the full spatial entanglement is indeed accessible experimentally; i.e., we have found practicable radial detection modes with negligible cross correlations. This allows us to demonstrate hybrid azimuthal-radial quantum correlations in a Hilbert space with more than 100 dimensions per photon.
Abstract It is well known that photons can carry a spatial structure akin to a ‘twisted’ or ‘rippled’ wavefront. Such structured light fields have sparked significant interest in both classical and quantum physics, with applications ranging from dense communications to light–matter interaction. Harnessing the full advantage of transverse spatial photonic encoding using the Laguerre–Gaussian (LG) basis in the quantum domain requires control over both the azimuthal (twisted) and radial (rippled) components of photons. However, precise measurement of the radial photonic degree-of-freedom has proven to be experimentally challenging primarily due to its transverse amplitude structure. Here we demonstrate the generation and certification of full-field LG entanglement between photons pairs generated by spontaneous parametric down conversion in the telecom regime. By precisely tuning the optical system parameters for state generation and collection, and adopting recently developed techniques for precise spatial mode measurement, we are able to certify fidelities up to 85% and entanglement dimensionalities up to 26 in a 43-dimensional radial and azimuthal LG mode space. Furthermore, we study two-photon quantum correlations between nine LG mode groups, demonstrating a correlation structure related to mode group order and inter-modal cross-talk. In addition, we show how the noise-robustness of high-dimensional entanglement certification can be significantly increased by using measurements in multiple LG mutually unbiased bases. Our work demonstrates the potential offered by the full spatial structure of the two-photon field for enhancing technologies for quantum information processing and communication.
High-dimensional spatially entangled two-photon state generated by spontaneous parametric down-conversion process (SPDC) has become a promising resource for several quantum information science applications. For harnessing high-dimensional entanglement advantages, detection capability in the Schmidt basis is a necessity. Spatial entanglement has been explored in several modal bases, such as pixel, azimuthal, and radial modes. Among them, pixel and azimuthal entanglement have been widely utilized due to efficient access to their Schmidt modes, while radial-mode entanglement remains underexploited. This is because for radial coordinates, there is neither a Schmidt-decomposed form for the SPDC photons nor is there a technique for measuring high-dimensional radial Schmidt modes, which is a major roadblock in harnessing radial mode advantages. In this work, we first theoretically show that the azimuthal averaging of SPDC two-photon state yields a radial Schmidt-decomposed form under typical experimental situations. We then demonstrate an innovative approach for extracting the radial Schmidt modes and their spectrum by characterizing the density matrix in the radial basis of one of the SPDC photons. Finally, we report the first-ever measurement of radial Schmidt spectrum of upto 50 radial Schmidt modes with about 98\% fidelity.
Abstract High-dimensional spatially entangled two-photon states generated by the spontaneous parametric down-conversion process (SPDC) have become a promising resource for several quantum information science applications. In order to harness high-dimensional entanglement advantages, detection capability in the Schmidt basis is a necessity. Spatial entanglement has been explored in several modal bases, such as pixel, azimuthal, and radial modes. Among them, pixel and azimuthal entanglement have been widely utilized due to efficient access to their Schmidt modes, while radial-mode entanglement remains underexploited. This is due to radial coordinates not having a Schmidt-decomposed form for the SPDC photons or a technique for measuring high-dimensional radial Schmidt modes, which is a major roadblock in harnessing radial mode advantages. In this work, we first theoretically show that azimuthal averaging of SPDC two-photon states yields a radial Schmidt-decomposed form under typical experimental situations. We then demonstrate an innovative approach for extracting the radial Schmidt modes and their spectrum by characterizing the density matrix in the radial basis of one of the SPDC photons. Finally, we report the first-ever measurement of the radial Schmidt spectrum of up to 50 radial Schmidt modes with about 98% fidelity.
Laguerre–Gaussian (LG) modes are characterized by two integer parameters, p and l , which correspond to the radial and azimuthal modes of photons. Both degrees of freedom are discrete and high-dimensional, and each can be used to construct a high-dimensional Hilbert space. Here, we use the radial-azimuthal modes of a single photon to construct two-dimensional and four-dimensional Bell states and experimentally realize full single-photon Bell-state characterization, thereby verifying the orthogonality and completeness of the Bell states. Subsequently, we measure the magnitude and phase of a four-dimensional superposition state in a 16-dimensional Hilbert space, obtaining results in good agreement with theoretical predictions, which further confirms the completeness of the four-dimensional Bell basis. Our experiment demonstrates that the radial and azimuthal modes of a single photon play equally important roles. Multiplexing these two degrees of freedom enables the construction of higher-dimensional Hilbert spaces and significantly enhances the information-carrying capacity of a single photon. Our results hold potential applications in the development of quantum communication protocols with high channel capacity.
Spontaneous parametric downconversion is the primary source to generate entangled photon pairs in quantum photonics laboratories. Depending on the experimental design, the generated photon pairs can be correlated in the frequency spectrum, polarization, position-momentum, and spatial modes. Exploring the spatial modes' correlation has hitherto been limited to the polar coordinates' azimuthal angle, and a few attempts to study Walsh mode's radial states. Here, we study the full-mode correlation, on a Laguerre-Gauss basis, between photon pairs generated in a type-I crystal. Furthermore, we explore the effect of a structured pump beam possessing different spatial modes onto bi-photon spatial correlation. Finally, we use the capability to project over arbitrary spatial mode superpositions to perform the bi-photon state's full quantum tomography in a 16-dimensional subspace.