{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BPSGTJOAVM3XLKVFWUIG7HMOCH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"187446201438d8c20ca7aa26fdd1c4d27d6a989d62a51015265a385090ad810f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-12T13:57:08Z","title_canon_sha256":"6ec53a30ec8fdab682391dea3ae89b76d8066d458ba3a64e5a1f1e3767e5520a"},"schema_version":"1.0","source":{"id":"1810.05522","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05522","created_at":"2026-05-17T23:54:10Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05522v2","created_at":"2026-05-17T23:54:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05522","created_at":"2026-05-17T23:54:10Z"},{"alias_kind":"pith_short_12","alias_value":"BPSGTJOAVM3X","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BPSGTJOAVM3XLKVF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BPSGTJOA","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:1fa0394b56b879180eba91300cb5249f0b902130facfb08efc11ffb94907814e","target":"graph","created_at":"2026-05-17T23:54:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For multipartite states we consider a notion of D-symmetry. For a system of $N$ qubits it concides with usual permutational symmetry. In case of $N$ qudits ($d\\geq 3$) the D-symmetry is stronger than the permutational one. For the space of all D-symmetric vectors in $(\\mathbb{C}^d)^{\\otimes N}$ we define a basis composed of vectors $\\{|R_{N,d;k}\\rangle: \\,0\\leq k\\leq N(d-1)\\}$ which are analog for Dicke states. The aim of this paper is to discuss the problem of separability of D-symmetric states which are diagonal in the basis $\\{|R_{N,d;k}\\rangle\\}$. We show that if $N$ is even and $d\\geq 2$ ","authors_text":"Adam Rutkowski, Marcin Marciniak, Michal Banacki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-12T13:57:08Z","title":"Necessary and sufficient condition of separability for D-symmetric diagonal states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05522","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:473fd1596df232c5a66b2f51b8b9f1d390198751fb8b0d766f64ab9065bc7695","target":"record","created_at":"2026-05-17T23:54:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"187446201438d8c20ca7aa26fdd1c4d27d6a989d62a51015265a385090ad810f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-12T13:57:08Z","title_canon_sha256":"6ec53a30ec8fdab682391dea3ae89b76d8066d458ba3a64e5a1f1e3767e5520a"},"schema_version":"1.0","source":{"id":"1810.05522","kind":"arxiv","version":2}},"canonical_sha256":"0be469a5c0ab3775aaa5b5106f9d8e11c14379f4ab9b317ed9ce8c76fe203c96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0be469a5c0ab3775aaa5b5106f9d8e11c14379f4ab9b317ed9ce8c76fe203c96","first_computed_at":"2026-05-17T23:54:10.774166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:10.774166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OMbIHv7O7TwtD+XMQiDCYdwrBDPcClLcnV1XL11tgpe91hWmWxicJMUF17+tNCGT08B26b8RPFt3MZgmHRXeAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:10.774949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05522","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:473fd1596df232c5a66b2f51b8b9f1d390198751fb8b0d766f64ab9065bc7695","sha256:1fa0394b56b879180eba91300cb5249f0b902130facfb08efc11ffb94907814e"],"state_sha256":"49ff75265d9625b60820b387755206eb5fb5faafe6872b2c2599e71bb0bba21d"}