{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GWDBTPQFXRLLV4IKOKR73V6ZQW","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":"ed63c92a9371ab71d9c380af87780a9b10ec89eb4240d0fb998d184d491a0bc5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-03-12T19:20:27Z","title_canon_sha256":"5b61371bf5be28570c69f9340d5ec026e8a14b1eecdd2324c3717f22e6b44442"},"schema_version":"1.0","source":{"id":"1403.3069","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3069","created_at":"2026-05-18T02:49:09Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3069v2","created_at":"2026-05-18T02:49:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3069","created_at":"2026-05-18T02:49:09Z"},{"alias_kind":"pith_short_12","alias_value":"GWDBTPQFXRLL","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GWDBTPQFXRLLV4IK","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GWDBTPQF","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:3a5136858ff12aefefc8d8bf2d8c2f112710bad6fce669e08c25a291efe21592","target":"graph","created_at":"2026-05-18T02:49:09Z","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":"We investigate which pure states of $n$ photons in $d$ modes can be transformed into each other via linear optics, without post-selection. In other words, we study the local unitary (LU) equivalence classes of symmetric many-qudit states. Writing our state as $f^\\dagger|\\Omega\\rangle$, with $f^\\dagger$ a homogeneous polynomial in the mode creation operators, we propose two sets of LU-invariants: (a) spectral invariants, which are the eigenvalues of the operator $ff^\\dagger$, and (b) moments, each given by the norm of the symmetric component of a tensor power of the initial state, which can be ","authors_text":"Javier Rodr\\'iguez-Laguna, Maciej Lewenstein, Micha{\\l} Oszmaniec, Piotr Migda{\\l}","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-03-12T19:20:27Z","title":"Which multiphoton states are related via linear optics?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3069","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:d29af9012f0cc3185627586d8d89c75332e998ebc143331f8a0798f887b0c06b","target":"record","created_at":"2026-05-18T02:49:09Z","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":"ed63c92a9371ab71d9c380af87780a9b10ec89eb4240d0fb998d184d491a0bc5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-03-12T19:20:27Z","title_canon_sha256":"5b61371bf5be28570c69f9340d5ec026e8a14b1eecdd2324c3717f22e6b44442"},"schema_version":"1.0","source":{"id":"1403.3069","kind":"arxiv","version":2}},"canonical_sha256":"358619be05bc56baf10a72a3fdd7d98589ac87549dc9e68637dbce925ddd295e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"358619be05bc56baf10a72a3fdd7d98589ac87549dc9e68637dbce925ddd295e","first_computed_at":"2026-05-18T02:49:09.608014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:09.608014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CsfWPRSm0XtqHFGfge+FSC2TE2AV+qJwBOOh4tXXOunsT5RBJGaeBKJ1Lu3YFCKisIzVi/Vr4aMjO1zJ0NURCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:09.608517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3069","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d29af9012f0cc3185627586d8d89c75332e998ebc143331f8a0798f887b0c06b","sha256:3a5136858ff12aefefc8d8bf2d8c2f112710bad6fce669e08c25a291efe21592"],"state_sha256":"1013f84bb48074c5a6edf2c2b9fa61c380e2fe8d00ff46555dbd9788847b2170"}