{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2EG56MWLC2S3VFFEPUOUJTFBZW","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":"50ca5eb2b243fa6f9e1d3ab033d5dcd4dad4a79089cbfa7163758c554bdd4cbf","cross_cats_sorted":["math-ph","math.MP","physics.app-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-05-06T08:38:28Z","title_canon_sha256":"938442cc6bd2cbac597147072c49e882e1d5b70253181fde9221df55edc83394"},"schema_version":"1.0","source":{"id":"1905.01878","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01878","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01878v1","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01878","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"pith_short_12","alias_value":"2EG56MWLC2S3","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2EG56MWLC2S3VFFE","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2EG56MWL","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:7f794c0a78fe1756ffb18554236c4eff429c3192442edf99d5acdfc66988cab4","target":"graph","created_at":"2026-05-17T23:46:57Z","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":"Probabilistically creating n perfect clones from m copies for one of N priori known quantum states with minimum failure probability is a long-standing problem. We provide a rigorous proof for the geometric approach to this probabilistic quantum cloning problem when N = 2. Then, we give the general geometric form of the sufficient and necessary condition of probabilistic cloning for N known quantum states. By this general geometric approach, we realize the optimal probabilistic quantum cloning of N known quantum states with priori probabilities. The results are also applicable to the identifica","authors_text":"Haixin Liu, Heng Fan","cross_cats":["math-ph","math.MP","physics.app-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-05-06T08:38:28Z","title":"Probabilistic quantum cloning of N quantum states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01878","kind":"arxiv","version":1},"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:c43a8a9f5e9fca485a5bba35efb1f2363f4425bf96b3af3050ae60355fe36662","target":"record","created_at":"2026-05-17T23:46:57Z","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":"50ca5eb2b243fa6f9e1d3ab033d5dcd4dad4a79089cbfa7163758c554bdd4cbf","cross_cats_sorted":["math-ph","math.MP","physics.app-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-05-06T08:38:28Z","title_canon_sha256":"938442cc6bd2cbac597147072c49e882e1d5b70253181fde9221df55edc83394"},"schema_version":"1.0","source":{"id":"1905.01878","kind":"arxiv","version":1}},"canonical_sha256":"d10ddf32cb16a5ba94a47d1d44cca1cd81314d11b8c455acbf306aac0d362362","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d10ddf32cb16a5ba94a47d1d44cca1cd81314d11b8c455acbf306aac0d362362","first_computed_at":"2026-05-17T23:46:57.141856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:57.141856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5K+FOY/RPpDtmehR1NTiOc/0QoCwIjmEzwdEpS1RkouXn3N5JRWoN4du5SwLc9OPndPeWMEdMd2QIUqn+lYMCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:57.142524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01878","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c43a8a9f5e9fca485a5bba35efb1f2363f4425bf96b3af3050ae60355fe36662","sha256:7f794c0a78fe1756ffb18554236c4eff429c3192442edf99d5acdfc66988cab4"],"state_sha256":"2a5be6db8849bbb0a8b8c514e3cf7c5e6e185e5b189b3a67d679a91be66900e5"}