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

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. By introducing the spin-orbital coupling into a folded geometric cavity, a group of classical non-separable states with three degrees of freedom are generated and controlled directly from a laser. The high-dimensional non-separable laser states can fully emulate the three-particle entangled Greenberger-Horne-Zeilinger (GHZ) states, which are experimentally verified by a proposed quantum-like state tomography method to reconstruct density matrices and calculate fidelities, providing a compact "at-the-source" solution of high-dimensional quantum-classical simulations and informatics.image