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Combining these degrees of freedom produces hybrid spin\u2013orbit states that live in a high-dimensional Hilbert space, offering greater information capacity and robustness for optical communication, quantum technologies, and metrology. However, generating arbitrary states in these spaces and characterizing them efficiently has remained difficult. Here we show a compact metasurface that generates arbitrary spin\u2013orbit states in a four-dimensional Hilbert space, visualized on a Poincar\u00e9 hypersphere, with straightforward scalability to higher dimensions. Using a tetratomic unit cell, the single-layer device precisely controls complex amplitude, phase, and polarization. We further introduce an efficient interferometric scheme that reconstructs the full density matrix of any\n                    <jats:italic>N<\/jats:italic>\n                    -dimensional spin\u2013orbit state using only three interferograms. This approach uncovers an intrinsic spin\u2013orbit parity order that governs the symmetry of projected intensity patterns, independent of the weighting of the eigenmodes, and enables controlled mode transformations through higher-order geometric phases. These advances establish a versatile platform for high-dimensional photonic technologies.\n                  <\/jats:p>","DOI":"10.1038\/s41467-026-74192-9","type":"journal-article","created":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T13:26:41Z","timestamp":1782307601000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Generic generation and manipulation of high-dimensional spin-orbit states in Hilbert space"],"prefix":"10.1038","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-7113-2506","authenticated-orcid":false,"given":"Peijin","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruizhe","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yang","family":"Cui","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3723-9632","authenticated-orcid":false,"given":"Guangzhou","family":"Geng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1508-9891","authenticated-orcid":false,"given":"Junjie","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6559-8101","authenticated-orcid":false,"given":"Xifeng","family":"Ren","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunkun","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9422-0888","authenticated-orcid":false,"given":"Yongtian","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4556-2333","authenticated-orcid":false,"given":"Shuang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3647-2128","authenticated-orcid":false,"given":"Lingling","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,24]]},"reference":[{"key":"74192_CR1","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1038\/s41566-021-00880-1","volume":"15","author":"X Ouyang","year":"2021","unstructured":"Ouyang, X. et al. 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