Balanced mode filtering for scalable Pauli-X gates in high-dimensional OAM space

The orbital angular momentum (OAM) of photons provides a pivotal resource for carrying out high-dimensional quantum Pauli-X operations due to its unique discrete infinite orthogonality, which opens enticing perspectives for high-capacity quantum communication and multi-parallel quantum computation. However, the state-of-the-art Pauli-X gates that require cyclic transformation of OAM modes are mostly limited to four modes, face scalability challenges owing to the system redundancy and fidelity degradation induced by increased processing modes. Here, we propose a general strategy to design scalable quantum Pauli-X gates in high-dimensional OAM space by taking full advantage of the order-correlated spatial divergence property of OAM modes. Leveraging the mechanism of balance mode filtering, partitioned phase is embedded between two structurally symmetric Q-plate elements that enable bidirectional mode shifting to filter out the highest-order OAM mode for spatially selective phase modulation. Derived from radial matching between modes and partitioned phase profiles, this design of parallel mode transformation underpins the extension to higher dimensions by merely adjusting filter parameters. We demonstrate the five-mode cyclic transformation with mode purity and diffraction efficiency higher than 92% and 92.7%, respectively. By incorporating polarization-entangled photon sources, we further realize five-dimensional quantum Pauli-X gates encoded on OAM space and experimentally verify the entanglement of output mode states. Low modulation loss and efficient quantum state tomography (QST) techniques endow the reconstructed density matrices with fidelities exceeding 92.3% ± 0.1%, indicating the well-performed entanglement preservation of output states. These results confirm that our approach achieves scalable quantum Pauli-X gate operations through a simple balanced architecture with high coherence, consolidating a theoretical and experimental foundation for large-scale quantum computation encoded on high-dimensional OAM space.