{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:HJE6F5HTTAOAS2DBQTKPRQV3C4","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":"aaa746785741efe975193afc190a4a1edf2bb1614c9b7863d52939a0fc5eb88c","cross_cats_sorted":["physics.optics"],"license":"","primary_cat":"quant-ph","submitted_at":"2007-12-07T18:02:19Z","title_canon_sha256":"8599c54ddca32b5e8d6a673e4eb91dc33737e8cc48e0d0262d74d21b81aba7b5"},"schema_version":"1.0","source":{"id":"0712.1197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1197","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1197v2","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1197","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"HJE6F5HTTAOA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"HJE6F5HTTAOAS2DB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"HJE6F5HT","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:93058b423ee66a211a77a6112f67ba1cdc6fedfe7dc89ad14530694fb9ace431","target":"graph","created_at":"2026-05-18T04:30:03Z","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":"Controlled generation and manipulation of photon states encoded in their spatial degrees of freedom is a crucial ingredient in many quantum information tasks exploiting higher-than-two dimensional encoding. Here, we prove the impossibility to arbitrarily modify $d$-level state superpositions (qu$d$its) for $d>2$, encoded in the transverse modes of light, with optical components associated to the group of symplectic transforms (Gaussian operations). Surprisingly, we also provide an explicit construction of how non-Gaussian operations acting on mode subspaces do enable to overcome the limit $d=2","authors_text":"Antonio Pic\\'on, Gabriel F. Calvo","cross_cats":["physics.optics"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2007-12-07T18:02:19Z","title":"Manipulation of single-photon states encoded in transverse spatial modes: possible and impossible tasks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1197","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:f692d4fda5c46c3b6214367f346a240e283ae158dbf6f28b37b74ae223c55535","target":"record","created_at":"2026-05-18T04:30:03Z","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":"aaa746785741efe975193afc190a4a1edf2bb1614c9b7863d52939a0fc5eb88c","cross_cats_sorted":["physics.optics"],"license":"","primary_cat":"quant-ph","submitted_at":"2007-12-07T18:02:19Z","title_canon_sha256":"8599c54ddca32b5e8d6a673e4eb91dc33737e8cc48e0d0262d74d21b81aba7b5"},"schema_version":"1.0","source":{"id":"0712.1197","kind":"arxiv","version":2}},"canonical_sha256":"3a49e2f4f3981c09686184d4f8c2bb1723c523d9a53744bd66a845f00e6e853e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a49e2f4f3981c09686184d4f8c2bb1723c523d9a53744bd66a845f00e6e853e","first_computed_at":"2026-05-18T04:30:03.128880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:03.128880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eNZbWAiu1qTjMmnq/bqJh2n/8JtDyJjmuvjAN1hM8gs92f9F8u84iMmB54Kc+NNZhNWclreD+eFRUSsKJys7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:03.129402Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.1197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f692d4fda5c46c3b6214367f346a240e283ae158dbf6f28b37b74ae223c55535","sha256:93058b423ee66a211a77a6112f67ba1cdc6fedfe7dc89ad14530694fb9ace431"],"state_sha256":"c498c0002f92639eed244fe72114cc4173aa6123e46aaaf88e41a70301d110f1"}