{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PMSCCWBYHGYH7KFYF37QVUIO5U","short_pith_number":"pith:PMSCCWBY","schema_version":"1.0","canonical_sha256":"7b2421583839b07fa8b82eff0ad10eed33359ceae0ef11b4d216f7aea9fb43b4","source":{"kind":"arxiv","id":"1807.08779","version":1},"attestation_state":"computed","paper":{"title":"A quantum Johnson-Lindenstrauss lemma via unitary t-designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Pranab Sen","submitted_at":"2018-07-23T18:38:35Z","abstract_excerpt":"The famous Johnson-Lindenstrauss lemma states that for any set of n vectors, there is a linear transformation into a space of dimension O(log n) that approximately preserves all their lengths. In fact, a Haar random unitary transformation followed by projection onto the first O(log n) coordinates followed by a scaling works as a valid transformation with high probability. In this work, we show that the Haar random unitary can be replaced by a uniformly random unitary chosen from a finite set called an approximate unitary t-design for t = O(log n). Choosing a unitary from such a design requires"},"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":"1807.08779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-23T18:38:35Z","cross_cats_sorted":[],"title_canon_sha256":"241d488c226a2a571d4610d2abbeea12b701948da7f236f0e77baef69e944481","abstract_canon_sha256":"f0c356100517507e1aefacc9d9af62252397508ca766cf0ced3003b9c2763acb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:57.886208Z","signature_b64":"pLQg/Fvr4WLb42rQksiLnMsmsCa/lXHo2ObUzLcus1KkcDaMRBf25gyzfyGYQsudJKh4yC/vZgW7CWp+qdEIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b2421583839b07fa8b82eff0ad10eed33359ceae0ef11b4d216f7aea9fb43b4","last_reissued_at":"2026-05-18T00:09:57.885376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:57.885376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A quantum Johnson-Lindenstrauss lemma via unitary t-designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Pranab Sen","submitted_at":"2018-07-23T18:38:35Z","abstract_excerpt":"The famous Johnson-Lindenstrauss lemma states that for any set of n vectors, there is a linear transformation into a space of dimension O(log n) that approximately preserves all their lengths. In fact, a Haar random unitary transformation followed by projection onto the first O(log n) coordinates followed by a scaling works as a valid transformation with high probability. In this work, we show that the Haar random unitary can be replaced by a uniformly random unitary chosen from a finite set called an approximate unitary t-design for t = O(log n). Choosing a unitary from such a design requires"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08779","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.08779","created_at":"2026-05-18T00:09:57.885522+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.08779v1","created_at":"2026-05-18T00:09:57.885522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08779","created_at":"2026-05-18T00:09:57.885522+00:00"},{"alias_kind":"pith_short_12","alias_value":"PMSCCWBYHGYH","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"PMSCCWBYHGYH7KFY","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"PMSCCWBY","created_at":"2026-05-18T12:32:46.962924+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PMSCCWBYHGYH7KFYF37QVUIO5U","json":"https://pith.science/pith/PMSCCWBYHGYH7KFYF37QVUIO5U.json","graph_json":"https://pith.science/api/pith-number/PMSCCWBYHGYH7KFYF37QVUIO5U/graph.json","events_json":"https://pith.science/api/pith-number/PMSCCWBYHGYH7KFYF37QVUIO5U/events.json","paper":"https://pith.science/paper/PMSCCWBY"},"agent_actions":{"view_html":"https://pith.science/pith/PMSCCWBYHGYH7KFYF37QVUIO5U","download_json":"https://pith.science/pith/PMSCCWBYHGYH7KFYF37QVUIO5U.json","view_paper":"https://pith.science/paper/PMSCCWBY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.08779&json=true","fetch_graph":"https://pith.science/api/pith-number/PMSCCWBYHGYH7KFYF37QVUIO5U/graph.json","fetch_events":"https://pith.science/api/pith-number/PMSCCWBYHGYH7KFYF37QVUIO5U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PMSCCWBYHGYH7KFYF37QVUIO5U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PMSCCWBYHGYH7KFYF37QVUIO5U/action/storage_attestation","attest_author":"https://pith.science/pith/PMSCCWBYHGYH7KFYF37QVUIO5U/action/author_attestation","sign_citation":"https://pith.science/pith/PMSCCWBYHGYH7KFYF37QVUIO5U/action/citation_signature","submit_replication":"https://pith.science/pith/PMSCCWBYHGYH7KFYF37QVUIO5U/action/replication_record"}},"created_at":"2026-05-18T00:09:57.885522+00:00","updated_at":"2026-05-18T00:09:57.885522+00:00"}