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:2609.38580

Algebraic Characterization of Biphoton Spatial-Mode Entanglement in Higher-Order Laguerre--Gaussian-Pumped SPDC

Takumi Jinushi, Hirokazu Kobayashi

quant-phSubmitted Sep 29, 2026• Announced Oct 1, 2026• 0 citations
arXivHTMLPDF

Abstract

High-dimensional spatial entanglement generated via spontaneous parametric down-conversion (SPDC) provides a powerful resource for quantum information processing, yet its mode structure becomes increasingly complex when the pump occupies a higher-order Laguerre--Gaussian (LG) mode. Here, we develop an algebraic framework for characterizing biphoton spatial-mode entanglement by factorizing LG-pumped SPDC into a spatial-mode beam-splitter transformation followed by spatial two-mode squeezing. By choosing the biphoton LG basis radius as the geometric mean of the pump-beam radius and the crystal-induced correlation width, we obtain a natural modal basis in which the two operations can be treated separately. When the pump-beam radius matches the correlation width, spatial squeezing vanishes, and the two circular-mode components of the pump are independently conserved across the signal and idler photons, leading to conservation of both orbital angular momentum and the total spatial mode number. We further derive an analytical expression for the Schmidt number for arbitrary LG pump modes and squeezing strengths, revealing how the radial and azimuthal pump indices govern the dimensionality of the spatial entanglement. This algebraic characterization provides a unified description of the mode structure, conservation laws, and entanglement dimensionality of higher-order-LG-pumped SPDC.

Comments
15 pages, 5 figures

Related papers

Unveiling quantum correlations of SPDC biphoton spatial modes using spatial light modulator

Omshankar, Vivek Venkataraman, Joyee Ghosh

Abstract We experimentally demonstrate the quantum entanglement in various spatial modes of the correlated photons generated via spontaneous parametric down-conversion in a type-II phase-matched periodically-poled KTP crystal. The two-fold coincidence measurement reveals the spatial entanglement between the photon pairs by projecting one of the correlated photons onto a Gaussian mode while scanning the spatial mode of its partner photon through selective projection (Gaussian, Laguerre–Gaussian (LG), Bessel-Gaussian (BG), and Airy–Gaussian (AG)) using a spatial light modulator (SLM). We also show the spatially resolved measurement of the non-conservation of orbital angular momentum via modal decomposition of the correlated photon in LG and BG bases.

Journal of Optics•Oct 22, 2024•3 citations

Enhanced entanglement from Ince-Gaussian pump beams in spontaneous parametric down-conversion

Baghdasar Baghdasaryan, S. Fritzsche

Spontaneous parametric down-conversion (SPDC) has been a reliable process for the generation of entangled photon pairs. In this process, a nonlinear quadratic crystal is pumped by a laser field in order to convert (high-energy) photons into correlated photon pairs whose efficient control plays an essential role in various applications of quantum information processing. In particular, the amount of entanglement has been successfully controlled by adjusting the spatial structure of the incident pump field. Here, we theoretically analyze how the entanglement of the down-converted two-photon state can be further enhanced by using Ince-Gaussian beams with well-defined ellipticity $\ensuremath{\epsilon}$, i.e., solutions of the paraxial wave equation in elliptical coordinates. These spatially structured beams are quite universal as they include both the Laguerre-Gaussian beams for $\ensuremath{\epsilon}\ensuremath{\rightarrow}0$ as well as the Hermite-Gaussian beams for $\ensuremath{\epsilon}\ensuremath{\rightarrow}\ensuremath{\infty}$. We demonstrate that the entanglement of the generated photon pairs in SPDC can be maximized by a proper choice of $\ensuremath{\epsilon}$ and that such an enhanced entanglement can be observed experimentally in terms of the Schmidt number.

Physical Review A•Nov 11, 2020•29 citations

Engineering the orbital angular momentum spectrum of down-converted photons using a mode-invariant pump

Anindya Banerji, Ali Anwar, Hrushikesh Sable +2 more

Abstract In this work, we investigate the orbital angular momentum (OAM) spectrum of photons generated via spontaneous parametric down-conversion (SPDC) and study how shaping the transverse profile of the pump beam influences the resulting spectrum. Using a perfect optical vortex (POV) mode as the pump, we show that the OAM spectrum narrows significantly, leading to purer OAM states. We further examine the entanglement between the down-converted photons in the OAM basis, finding that Laguerre–Gaussian (LG) pumped photons exhibit increased higher-dimensional entanglement at the expense of mode purity.

Physica Scripta•Nov 21, 2025•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

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

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
High-dimensional spatial entanglement generated via spontaneous parametric down-conversion (SPDC) provides a powerful resource for quantum information processing, yet its mode structure becomes increasingly complex when the pump occupies a higher-order Laguerre--Gaussian (LG) mode. Here, we develop an algebraic framework for characterizing biphoton spatial-mode entanglement by factorizing LG-pumped SPDC into a spatial-mode beam-splitter transformation followed by spatial two-mode squeezing. By choosing the biphoton LG basis radius as the geometric mean of the pump-beam radius and the crystal-induced correlation width, we obtain a natural modal basis in which the two operations can be treated separately. When the pump-beam radius matches the correlation width, spatial squeezing vanishes, and the two circular-mode components of the pump are independently conserved across the signal and idler photons, leading to conservation of both orbital angular momentum and the total spatial mode number. We further derive an analytical expression for the Schmidt number for arbitrary LG pump modes and squeezing strengths, revealing how the radial and azimuthal pump indices govern the dimensionality of the spatial entanglement. This algebraic characterization provides a unified description of the mode structure, conservation laws, and entanglement dimensionality of higher-order-LG-pumped SPDC.
Abstract We experimentally demonstrate the quantum entanglement in various spatial modes of the correlated photons generated via spontaneous parametric down-conversion in a type-II phase-matched periodically-poled KTP crystal. The two-fold coincidence measurement reveals the spatial entanglement between the photon pairs by projecting one of the correlated photons onto a Gaussian mode while scanning the spatial mode of its partner photon through selective projection (Gaussian, Laguerre–Gaussian (LG), Bessel-Gaussian (BG), and Airy–Gaussian (AG)) using a spatial light modulator (SLM). We also show the spatially resolved measurement of the non-conservation of orbital angular momentum via modal decomposition of the correlated photon in LG and BG bases.
Spontaneous parametric down-conversion (SPDC) has been a reliable process for the generation of entangled photon pairs. In this process, a nonlinear quadratic crystal is pumped by a laser field in order to convert (high-energy) photons into correlated photon pairs whose efficient control plays an essential role in various applications of quantum information processing. In particular, the amount of entanglement has been successfully controlled by adjusting the spatial structure of the incident pump field. Here, we theoretically analyze how the entanglement of the down-converted two-photon state can be further enhanced by using Ince-Gaussian beams with well-defined ellipticity $\ensuremath{\epsilon}$, i.e., solutions of the paraxial wave equation in elliptical coordinates. These spatially structured beams are quite universal as they include both the Laguerre-Gaussian beams for $\ensuremath{\epsilon}\ensuremath{\rightarrow}0$ as well as the Hermite-Gaussian beams for $\ensuremath{\epsilon}\ensuremath{\rightarrow}\ensuremath{\infty}$. We demonstrate that the entanglement of the generated photon pairs in SPDC can be maximized by a proper choice of $\ensuremath{\epsilon}$ and that such an enhanced entanglement can be observed experimentally in terms of the Schmidt number.
Abstract In this work, we investigate the orbital angular momentum (OAM) spectrum of photons generated via spontaneous parametric down-conversion (SPDC) and study how shaping the transverse profile of the pump beam influences the resulting spectrum. Using a perfect optical vortex (POV) mode as the pump, we show that the OAM spectrum narrows significantly, leading to purer OAM states. We further examine the entanglement between the down-converted photons in the OAM basis, finding that Laguerre–Gaussian (LG) pumped photons exhibit increased higher-dimensional entanglement at the expense of mode purity.
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.
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 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.