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We also construct a minimal set of generators of the algebra of polynomial $\\Un(6)$-invariants on $\\bwe^3(\\bC^6)$. It turns out that this algebra is isomorphic to the algebra of polynomial LU-invariants of three-qubits which are additionally invariant under qubit permutations. As a consequence of this surprising fact, we deduce that there is a one-to-one correspondence between the $\\Un(6)$-orbits "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1306.2570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-06-11T16:10:27Z","cross_cats_sorted":[],"title_canon_sha256":"e26f649ffc2ab5cb72afe93356273bad1377cdfd63af64b245298ebaaca08445","abstract_canon_sha256":"8ec6e4829a7aba8a08be0ca6bccd9afcb893bdc7df3979f3f83c9590508ae5c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:32.032466Z","signature_b64":"Wi11DGCwV4e48JrzM7X2PYxoleKIcwCiBXyrvXRdKuFUu4c/XilwRCLsMtn04tBdcEmTsS9DViiIZw+isXLvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22e5c395b532e0497117ca060263f4c8b300d2c32c206e6a4d38e3fa3c7e6672","last_reissued_at":"2026-05-18T02:45:32.031750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:32.031750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Canonical form of three-fermion pure-states with six single particle states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Bei Zeng, Dragomir Z Djokovic, Lin Chen, Markus Grassl","submitted_at":"2013-06-11T16:10:27Z","abstract_excerpt":"We construct a canonical form for pure states in $\\bwe^3(\\bC^6)$, the three-fermion system with six single particle states, under local unitary (LU) transformations, i.e., the unitary group $\\Un(6)$. We also construct a minimal set of generators of the algebra of polynomial $\\Un(6)$-invariants on $\\bwe^3(\\bC^6)$. It turns out that this algebra is isomorphic to the algebra of polynomial LU-invariants of three-qubits which are additionally invariant under qubit permutations. 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