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

Laser & Photonics Review

Intra‐Cavity Laser Manipulation of High‐Dimensional Non‐Separable States

Lan Hai, Zhejing Zhang, Shi-Long Liu, Lang Li, Zhi‐Yuan Zhou, Qing Wang, Yanze Gao, Chunqing Gao, Yijie Shen, Shiyao Fu

Published Nov 27, 2023• 30 citations
Publisher

Abstract

Abstract Non‐separable states of structured light have the analogous mathematical forms with quantum entanglement, which offer an effective way to simulate quantum process. However, the classical multi‐partite non‐separable states analogue to multi‐particle entanglements can only be controlled by bulky free‐space modulation of light through coupling multiple degrees of freedom (DoFs) with orbital angular momentum (OAM) to achieve high dimensionality and other DoFs to emulate multi‐parties. In this paper, a scheme is proposed to directly emit multi‐partite non‐separable states from a simple laser cavity to mimic multi‐particle quantum entanglement. Through manipulating three DoFs as OAM, polarization, and wavevector inside a laser cavity, the eight‐dimensional (8D) tripartite states and all Greenberger‐Horne‐Zeilinger (GHZ)‐like states can be generated and controlled on demand. In addition, an effective method is proposed to perform state tomography employing convolutional neural network (CNN), for measuring the generated GHZ‐like states with highest fidelity up to 95.11%. This work reveals a feasibility of intra‐cavity manipulation of high‐dimensional multipartite non‐separable states, opening a compact device for quantum‐classical analogy and paving the path for advanced quantum scenarios.

DOI
10.1002/lpor.202300593

Related papers

Intra‐Cavity Laser Manipulation of High‐Dimensional Non‐Separable States (Laser Photonics Rev. 18(4)/2024)

Lan Hai, Zhichao Zhang, Shi-Long Liu +7 more

High-Dimensional Non-Separable States In article 2300593, Lan Hai, Zhichao Zhang, Shiyao Fu, and co-workers propose a method to generate multi-partite non-separable states within a specially designed cavity. By introducing the coupling mechanism of spin angular momentum and orbital angular momentum (SAM-OAM) into a folded-cavity laser, a group of classical non-separable states combining three degrees of freedom are generated directly and well controlled. The non-separability of eight experimentally generated Greenberger–Horne–Zeilinger (GHZ)-like states, measured by a proposed state tomography method to reconstruct the density matrices and calculate fidelities, is verified and enables multiple quantum analogues tasks.

Laser & Photonics Review•Apr 1, 2024•0 citations

Creation and control of high-dimensional multi-partite classically entangled light

Yijie Shen, Isaac M. Nape, Xilin Yang +4 more

Vector beams, non-separable in spatial mode and polarisation, have emerged as enabling tools in many diverse applications, from communication to imaging. This applicability has been achieved by sophisticated laser designs controlling the spin and orbital angular momentum, but so far is restricted to only two-dimensional states. Here we demonstrate the first vectorially structured light created and fully controlled in eight dimensions, a new state-of-the-art. We externally modulate our beam to control, for the first time, the complete set of classical Greenberger-Horne-Zeilinger (GHZ) states in paraxial structured light beams, in analogy with high-dimensional multi-partite quantum entangled states, and introduce a new tomography method to verify their fidelity. Our complete theoretical framework reveals a rich parameter space for further extending the dimensionality and degrees of freedom, opening new pathways for vectorially structured light in the classical and quantum regimes.

Light Science & Applications•Mar 8, 2021•109 citations

High-dimensional classically entangled light from a laser

Yijie Shen, Isaac M. Nape, Xilin Yang +4 more

Vectorially structured light has emerged as an enabling tool in many diverse applications, from communication to imaging, exploiting quantum-like correlations courtesy of a non-separable spatially varying polarization structure. Creating these states at the source remains challenging and is presently limited to two-dimensional vectorial states by customized lasers. Here we invoke ray-wave duality in a simple laser cavity to produce polarization marked multi-path modes that are non-separable in three degrees of freedom and in eight dimensions. As a topical example, we use our laser to produce the complete set of Greenberger-Horne-Zeilinger (GHZ) basis states, mimicking high-dimensional multi-partite entanglement with classical light, which we confirm by a new projection approach. We offer a complete theoretical framework for our laser based on SU(2) symmetry groups, revealing a rich parameter space for further exploitation. Our approach requires only a conventional laser with no special optical elements, is easily scaleable to higher dimensions, and offers a simple but elegant solution for at-the-source creation of classically entangled states of structured light, opening new applications in simulating and enhancing high-dimensional quantum systems.

arXiv:2002.01585•Feb 5, 2020•3 citations

Multipartite classically entangled scalar beams

Zhensong Wan, Yijie Shen, Qiang Liu +1 more

Classically entangled light is used to refer to a class of structured beams with space-polarization, polarization-time, and space-time non-separable states akin to entangled states, which enable novel quantum-analog methods and applications in structured light. Here, we argue that classical entanglement is also available for pure scalar beams with multiple non-separable spatial degrees of freedom (DoFs). We theoretically and experimentally demonstrate a class of scalar ray-wave structured light with multiple controllable local DoFs to emulate multipartite entangled states, including the Greenberger-Horne-Zeilinger states. Our work unveils a rich parameter space for high-dimensional and multi-DoF control of structured light to extend applications in classical-quantum regimes.

Optics Letters•Mar 8, 2022•16 citations

Observation of Genuine High-dimensional Multi-partite Non-locality in Entangled Photon States

Xiao‐Min Hu, Cen-Xiao Huang, Nicola d'Alessandro +10 more

Quantum information science has leaped forward with the exploration of high-dimensional quantum systems, offering greater potential than traditional qubits in quantum communication and quantum computing. To advance the field of high-dimensional quantum technology, a significant effort is underway to progressively enhance the entanglement dimension between two particles. An alternative effective strategy involves not only increasing the dimensionality but also expanding the number of particles that are entangled. We present an experimental study demonstrating multi-partite quantum non-locality beyond qubit constraints, thus moving into the realm of strongly entangled high-dimensional multi-particle quantum systems. In the experiment, quantum states were encoded in the path degree of freedom (DoF) and controlled via polarization, enabling efficient operations in a two-dimensional plane to prepare three- and four-particle Greenberger-Horne-Zeilinger (GHZ) states in three-level systems. Our experimental results reveal ways in which high-dimensional systems can surpass qubits in terms of violating local-hidden-variable theories. Our realization of multiple complex and high-quality entanglement technologies is an important primary step for more complex quantum computing and communication protocols. Experimental demonstrations of genuine high-dimensional multipartite quantum nonlocality have been lacking so far. Here, the authors fill this gap using entangled photons, surpassing qubit-based limits and paving the way for device-independent quantum information processing in more complex systems.

arXiv:2505.10035•Nature Communications•May 30, 2025•12 citations

Direct transfer of classical non-separable states into hybrid entangled two photon states

M. V. Jabir, N. Apurv Chaitanya, Manoj V. Mathew +1 more

Hybrid entangled states, having entanglement between different degrees-of-freedom (DoF) of a particle pair, are of great interest for quantum information science and communication protocols. Among different DoFs, the hybrid entangled states encoded with polarization and orbital angular momentum (OAM) allow the generation of qubit-qudit entangled states, macroscopic entanglement with very high quanta of OAM and improvement in angular resolution in remote sensing. Till date, such hybrid entangled states are generated by using a high-fidelity polarization entangled states and subsequent imprinting of chosen amount of OAM using suitable mode converters such as spatial light modulator in complicated experimental schemes. Given that the entangled sources have feeble number of photons, loss of photons during imprinting of OAM using diffractive optical elements limits the use of such hybrid states for practical applications. Here we report, on a simple generic experimental scheme to generate hybrid entangled states in polarization and OAM through direct transfer of classical non-separable states of the pump beam in parametric down conversion process. As a proof of principle, using local non-separable pump states of OAM mode l = 3, we have produced quantum hybrid entangled states with entanglement witness parameter of ~1.25 ± 0.03 violating by 8 standard deviation.

Scientific Reports•Jul 31, 2017•32 citations
Abstract Non‐separable states of structured light have the analogous mathematical forms with quantum entanglement, which offer an effective way to simulate quantum process. However, the classical multi‐partite non‐separable states analogue to multi‐particle entanglements can only be controlled by bulky free‐space modulation of light through coupling multiple degrees of freedom (DoFs) with orbital angular momentum (OAM) to achieve high dimensionality and other DoFs to emulate multi‐parties. In this paper, a scheme is proposed to directly emit multi‐partite non‐separable states from a simple laser cavity to mimic multi‐particle quantum entanglement. Through manipulating three DoFs as OAM, polarization, and wavevector inside a laser cavity, the eight‐dimensional (8D) tripartite states and all Greenberger‐Horne‐Zeilinger (GHZ)‐like states can be generated and controlled on demand. In addition, an effective method is proposed to perform state tomography employing convolutional neural network (CNN), for measuring the generated GHZ‐like states with highest fidelity up to 95.11%. This work reveals a feasibility of intra‐cavity manipulation of high‐dimensional multipartite non‐separable states, opening a compact device for quantum‐classical analogy and paving the path for advanced quantum scenarios.
High-Dimensional Non-Separable States In article 2300593, Lan Hai, Zhichao Zhang, Shiyao Fu, and co-workers propose a method to generate multi-partite non-separable states within a specially designed cavity. By introducing the coupling mechanism of spin angular momentum and orbital angular momentum (SAM-OAM) into a folded-cavity laser, a group of classical non-separable states combining three degrees of freedom are generated directly and well controlled. The non-separability of eight experimentally generated Greenberger–Horne–Zeilinger (GHZ)-like states, measured by a proposed state tomography method to reconstruct the density matrices and calculate fidelities, is verified and enables multiple quantum analogues tasks.
Vector beams, non-separable in spatial mode and polarisation, have emerged as enabling tools in many diverse applications, from communication to imaging. This applicability has been achieved by sophisticated laser designs controlling the spin and orbital angular momentum, but so far is restricted to only two-dimensional states. Here we demonstrate the first vectorially structured light created and fully controlled in eight dimensions, a new state-of-the-art. We externally modulate our beam to control, for the first time, the complete set of classical Greenberger-Horne-Zeilinger (GHZ) states in paraxial structured light beams, in analogy with high-dimensional multi-partite quantum entangled states, and introduce a new tomography method to verify their fidelity. Our complete theoretical framework reveals a rich parameter space for further extending the dimensionality and degrees of freedom, opening new pathways for vectorially structured light in the classical and quantum regimes.
Vectorially structured light has emerged as an enabling tool in many diverse applications, from communication to imaging, exploiting quantum-like correlations courtesy of a non-separable spatially varying polarization structure. Creating these states at the source remains challenging and is presently limited to two-dimensional vectorial states by customized lasers. Here we invoke ray-wave duality in a simple laser cavity to produce polarization marked multi-path modes that are non-separable in three degrees of freedom and in eight dimensions. As a topical example, we use our laser to produce the complete set of Greenberger-Horne-Zeilinger (GHZ) basis states, mimicking high-dimensional multi-partite entanglement with classical light, which we confirm by a new projection approach. We offer a complete theoretical framework for our laser based on SU(2) symmetry groups, revealing a rich parameter space for further exploitation. Our approach requires only a conventional laser with no special optical elements, is easily scaleable to higher dimensions, and offers a simple but elegant solution for at-the-source creation of classically entangled states of structured light, opening new applications in simulating and enhancing high-dimensional quantum systems.
Classically entangled light is used to refer to a class of structured beams with space-polarization, polarization-time, and space-time non-separable states akin to entangled states, which enable novel quantum-analog methods and applications in structured light. Here, we argue that classical entanglement is also available for pure scalar beams with multiple non-separable spatial degrees of freedom (DoFs). We theoretically and experimentally demonstrate a class of scalar ray-wave structured light with multiple controllable local DoFs to emulate multipartite entangled states, including the Greenberger-Horne-Zeilinger states. Our work unveils a rich parameter space for high-dimensional and multi-DoF control of structured light to extend applications in classical-quantum regimes.
Quantum information science has leaped forward with the exploration of high-dimensional quantum systems, offering greater potential than traditional qubits in quantum communication and quantum computing. To advance the field of high-dimensional quantum technology, a significant effort is underway to progressively enhance the entanglement dimension between two particles. An alternative effective strategy involves not only increasing the dimensionality but also expanding the number of particles that are entangled. We present an experimental study demonstrating multi-partite quantum non-locality beyond qubit constraints, thus moving into the realm of strongly entangled high-dimensional multi-particle quantum systems. In the experiment, quantum states were encoded in the path degree of freedom (DoF) and controlled via polarization, enabling efficient operations in a two-dimensional plane to prepare three- and four-particle Greenberger-Horne-Zeilinger (GHZ) states in three-level systems. Our experimental results reveal ways in which high-dimensional systems can surpass qubits in terms of violating local-hidden-variable theories. Our realization of multiple complex and high-quality entanglement technologies is an important primary step for more complex quantum computing and communication protocols. Experimental demonstrations of genuine high-dimensional multipartite quantum nonlocality have been lacking so far. Here, the authors fill this gap using entangled photons, surpassing qubit-based limits and paving the way for device-independent quantum information processing in more complex systems.
Hybrid entangled states, having entanglement between different degrees-of-freedom (DoF) of a particle pair, are of great interest for quantum information science and communication protocols. Among different DoFs, the hybrid entangled states encoded with polarization and orbital angular momentum (OAM) allow the generation of qubit-qudit entangled states, macroscopic entanglement with very high quanta of OAM and improvement in angular resolution in remote sensing. Till date, such hybrid entangled states are generated by using a high-fidelity polarization entangled states and subsequent imprinting of chosen amount of OAM using suitable mode converters such as spatial light modulator in complicated experimental schemes. Given that the entangled sources have feeble number of photons, loss of photons during imprinting of OAM using diffractive optical elements limits the use of such hybrid states for practical applications. Here we report, on a simple generic experimental scheme to generate hybrid entangled states in polarization and OAM through direct transfer of classical non-separable states of the pump beam in parametric down conversion process. As a proof of principle, using local non-separable pump states of OAM mode l = 3, we have produced quantum hybrid entangled states with entanglement witness parameter of ~1.25 ± 0.03 violating by 8 standard deviation.