{"paper":{"title":"Classification of four-rebit states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP","math.RT"],"primary_cat":"quant-ph","authors_text":"Alessio Marrani, Heiko Dietrich, Marcos Origlia, Willem A. de Graaf","submitted_at":"2022-01-27T19:40:21Z","abstract_excerpt":"We classify states of four rebits, that is, we classify the orbits of the group $\\widehat{G}(\\mathbb R) = \\mathrm{\\mathop{SL}}(2,\\mathbb R)^4$ in the space $(\\mathbb R^2)^{\\otimes 4}$. This is the real analogon of the well-known SLOCC operations in quantum information theory. By constructing the $\\widehat{G}(\\mathbb R)$-module $(\\mathbb R^2)^{\\otimes 4}$ via a $\\mathbb Z/2\\mathbb Z$-grading of the simple split real Lie algebra of type $D_4$, the orbits are divided into three groups: semisimple, nilpotent and mixed. The nilpotent orbits have been classified in Dietrich et al. (2017), yielding a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.11777","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.11777/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}