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Light Science & Applications

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

Yijie Shen, Isaac M. Nape, Xilin Yang, Xing Fu, Mali Gong, Darryl Naidoo, Andrew Forbes

Published Mar 8, 2021• 109 citations
Publisher

Abstract

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.

DOI
10.1038/s41377-021-00493-x

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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.
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.
Structured light has become topical of late, where controlling light in all its degrees of freedom has offered novel states of light long predicted, enhanced functionality in applications, and a modern toolbox for probing fundamental science. Structuring light as single photons and entangled states allows the spatial modes of light to be used to encode a large alphabet, accessing high dimensional Hilbert spaces for fundamental tests of quantum mechanics and improved quantum information processing tasks. In this tutorial, we outline the basic concepts of high dimensional quantum states expressed in a basis of spatial modes (structured light) and explain how to create, control, and detect such quantum states in the laboratory with a focus on transverse spatial modes such as the orbital angular momentum and pixel (position) modes. Finally, we highlight some example applications of such quantum structured light, from communications to imaging.
Entanglement in high-dimensional quantum systems, where one or more degrees of freedom of light are involved, offers increased information capacities and enables new quantum protocols.Here, we demonstrate a functional source of high-dimensional, noise-resilient hyperentangled states encoded in time-frequency and vector vortex structured modes, which in turn carry single-particle entanglement between polarization and orbital angular momentum.Pairing nonlinearity-engineered parametric downconversion in an interferometric scheme with spin-to-orbital-angular-momentum conversion, we generate highly entangled photon pairs at telecom wavelength that we characterize via two-photon interference and quantum state tomography, achieving near-unity visibilities and fidelities.While hyperentanglement has been demonstrated before in photonic qubits, here we present a rich entanglement structure involving spectrally and spatially structured light, where three different forms of entanglement coexist in the same biphoton state.